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The dataset generation failed
Error code: DatasetGenerationError
Exception: TypeError
Message: Couldn't cast array of type
struct<type: string, structure: string, num_compositions: int64, sub_equations: list<item: struct<variable: string, p: int64, q: int64, gcd: int64, description: string>>, final_gcd: int64, module_name: string, seed: int64, min_gcd_value: int64, max_gcd_value: int64, min_gcd_operand: int64, max_gcd_operand: int64, composition_structure: string>
to
{'type': Value('string'), 'structure': Value('string'), 'num_compositions': Value('int64'), 'sub_equations': List({'variable': Value('string'), 'dividend': Value('int64'), 'divisor': Value('int64'), 'remainder': Value('int64'), 'description': Value('string')}), 'final_dividend': Value('int64'), 'final_remainder': Value('int64'), 'module_name': Value('string'), 'seed': Value('int64'), 'min_dividend': Value('int64'), 'max_dividend': Value('int64'), 'min_divisor': Value('int64'), 'max_divisor': Value('int64'), 'composition_structure': Value('string')}
Traceback: Traceback (most recent call last):
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1831, in _prepare_split_single
writer.write_table(table)
File "/usr/local/lib/python3.12/site-packages/datasets/arrow_writer.py", line 714, in write_table
pa_table = table_cast(pa_table, self._schema)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2272, in table_cast
return cast_table_to_schema(table, schema)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2224, in cast_table_to_schema
cast_array_to_feature(
File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 1795, in wrapper
return pa.chunked_array([func(chunk, *args, **kwargs) for chunk in array.chunks])
^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2092, in cast_array_to_feature
raise TypeError(f"Couldn't cast array of type\n{_short_str(array.type)}\nto\n{_short_str(feature)}")
TypeError: Couldn't cast array of type
struct<type: string, structure: string, num_compositions: int64, sub_equations: list<item: struct<variable: string, p: int64, q: int64, gcd: int64, description: string>>, final_gcd: int64, module_name: string, seed: int64, min_gcd_value: int64, max_gcd_value: int64, min_gcd_operand: int64, max_gcd_operand: int64, composition_structure: string>
to
{'type': Value('string'), 'structure': Value('string'), 'num_compositions': Value('int64'), 'sub_equations': List({'variable': Value('string'), 'dividend': Value('int64'), 'divisor': Value('int64'), 'remainder': Value('int64'), 'description': Value('string')}), 'final_dividend': Value('int64'), 'final_remainder': Value('int64'), 'module_name': Value('string'), 'seed': Value('int64'), 'min_dividend': Value('int64'), 'max_dividend': Value('int64'), 'min_divisor': Value('int64'), 'max_divisor': Value('int64'), 'composition_structure': Value('string')}
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1339, in compute_config_parquet_and_info_response
parquet_operations = convert_to_parquet(builder)
^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 972, in convert_to_parquet
builder.download_and_prepare(
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 894, in download_and_prepare
self._download_and_prepare(
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 970, in _download_and_prepare
self._prepare_split(split_generator, **prepare_split_kwargs)
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1702, in _prepare_split
for job_id, done, content in self._prepare_split_single(
^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1858, in _prepare_split_single
raise DatasetGenerationError("An error occurred while generating the dataset") from e
datasets.exceptions.DatasetGenerationError: An error occurred while generating the datasetNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
prompt
string | ground_truth_answer
string | id
int64 | category
string | metadata
dict |
|---|---|---|---|---|
Let i be the remainder when 195 is divided by 13. Let b be the remainder when i + 617 is divided by 39. Let o be the remainder when b + 642 is divided by 13. Let s be the remainder when b + 786 is divided by 93. Let r be the remainder when s - o + 814 is divided by 63. Let k be the remainder when r + 474 is divided by 99. Let a be the remainder when k + 222 is divided by 45. Let y be the remainder when a + 170 is divided by 53. Let q be the remainder when y + 154 is divided by 58. Let m be the remainder when y + 673 is divided by 54. What is the remainder when q - m + 478 is divided by 43?
Please reason step by step, and put your final answer within \boxed{}.
|
14
| 0
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3, 4 -> 5 -> 6 -> 7 -> 8 -> 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "i",
"dividend": 195,
"divisor": 13,
"remainder": 0,
"description": "Let i be the remainder when 195 is divided by 13."
},
{
"variable": "b",
"dividend": 617,
"divisor": 39,
"remainder": 32,
"description": "Let b be the remainder when i + 617 is divided by 39."
},
{
"variable": "o",
"dividend": 674,
"divisor": 13,
"remainder": 11,
"description": "Let o be the remainder when b + 642 is divided by 13."
},
{
"variable": "s",
"dividend": 818,
"divisor": 93,
"remainder": 74,
"description": "Let s be the remainder when b + 786 is divided by 93."
},
{
"variable": "r",
"dividend": 877,
"divisor": 63,
"remainder": 58,
"description": "Let r be the remainder when s - o + 814 is divided by 63."
},
{
"variable": "k",
"dividend": 532,
"divisor": 99,
"remainder": 37,
"description": "Let k be the remainder when r + 474 is divided by 99."
},
{
"variable": "a",
"dividend": 259,
"divisor": 45,
"remainder": 34,
"description": "Let a be the remainder when k + 222 is divided by 45."
},
{
"variable": "y",
"dividend": 204,
"divisor": 53,
"remainder": 45,
"description": "Let y be the remainder when a + 170 is divided by 53."
},
{
"variable": "q",
"dividend": 199,
"divisor": 58,
"remainder": 25,
"description": "Let q be the remainder when y + 154 is divided by 58."
},
{
"variable": "m",
"dividend": 718,
"divisor": 54,
"remainder": 16,
"description": "Let m be the remainder when y + 673 is divided by 54."
}
],
"final_dividend": 487,
"final_remainder": 14,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let b be the remainder when 489 is divided by 22. Let p be the remainder when b + 745 is divided by 68. Let y be the remainder when b + 474 is divided by 30. Let g be the remainder when b + 781 is divided by 36. Let q be the remainder when y - p + g + 431 is divided by 99. Let c be the remainder when q + 8 is divided by 91. Let o be the remainder when c + 325 is divided by 17. Let i be the remainder when o + 499 is divided by 50. Let x be the remainder when o + 305 is divided by 18. Let z be the remainder when i - x + 371 is divided by 37. What is the remainder when z + 351 is divided by 27?
Please reason step by step, and put your final answer within \boxed{}.
|
1
| 1
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2, 3, 4 -> 5 -> 6 -> 7 -> 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "b",
"dividend": 489,
"divisor": 22,
"remainder": 5,
"description": "Let b be the remainder when 489 is divided by 22."
},
{
"variable": "p",
"dividend": 750,
"divisor": 68,
"remainder": 2,
"description": "Let p be the remainder when b + 745 is divided by 68."
},
{
"variable": "y",
"dividend": 479,
"divisor": 30,
"remainder": 29,
"description": "Let y be the remainder when b + 474 is divided by 30."
},
{
"variable": "g",
"dividend": 786,
"divisor": 36,
"remainder": 30,
"description": "Let g be the remainder when b + 781 is divided by 36."
},
{
"variable": "q",
"dividend": 488,
"divisor": 99,
"remainder": 92,
"description": "Let q be the remainder when y - p + g + 431 is divided by 99."
},
{
"variable": "c",
"dividend": 100,
"divisor": 91,
"remainder": 9,
"description": "Let c be the remainder when q + 8 is divided by 91."
},
{
"variable": "o",
"dividend": 334,
"divisor": 17,
"remainder": 11,
"description": "Let o be the remainder when c + 325 is divided by 17."
},
{
"variable": "i",
"dividend": 510,
"divisor": 50,
"remainder": 10,
"description": "Let i be the remainder when o + 499 is divided by 50."
},
{
"variable": "x",
"dividend": 316,
"divisor": 18,
"remainder": 10,
"description": "Let x be the remainder when o + 305 is divided by 18."
},
{
"variable": "z",
"dividend": 371,
"divisor": 37,
"remainder": 1,
"description": "Let z be the remainder when i - x + 371 is divided by 37."
}
],
"final_dividend": 352,
"final_remainder": 1,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let h be the remainder when 742 is divided by 29. Let k be the remainder when 532 is divided by 97. Let o be the remainder when 494 is divided by 18. Let g be the remainder when 579 is divided by 86. Let m be the remainder when 666 is divided by 42. Let d be the remainder when m - k - g + o - h + 186 is divided by 97. Let u be the remainder when d + 874 is divided by 74. Let y be the remainder when d + 202 is divided by 74. Let x be the remainder when y - u + 886 is divided by 91. Let j be the remainder when x + 836 is divided by 79. What is the remainder when j + 72 is divided by 77?
Please reason step by step, and put your final answer within \boxed{}.
|
23
| 2
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2, 3, 4, 5 -> 6 -> 7, 8 -> 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "h",
"dividend": 742,
"divisor": 29,
"remainder": 17,
"description": "Let h be the remainder when 742 is divided by 29."
},
{
"variable": "k",
"dividend": 532,
"divisor": 97,
"remainder": 47,
"description": "Let k be the remainder when 532 is divided by 97."
},
{
"variable": "o",
"dividend": 494,
"divisor": 18,
"remainder": 8,
"description": "Let o be the remainder when 494 is divided by 18."
},
{
"variable": "g",
"dividend": 579,
"divisor": 86,
"remainder": 63,
"description": "Let g be the remainder when 579 is divided by 86."
},
{
"variable": "m",
"dividend": 666,
"divisor": 42,
"remainder": 36,
"description": "Let m be the remainder when 666 is divided by 42."
},
{
"variable": "d",
"dividend": 103,
"divisor": 97,
"remainder": 6,
"description": "Let d be the remainder when m - k - g + o - h + 186 is divided by 97."
},
{
"variable": "u",
"dividend": 880,
"divisor": 74,
"remainder": 66,
"description": "Let u be the remainder when d + 874 is divided by 74."
},
{
"variable": "y",
"dividend": 208,
"divisor": 74,
"remainder": 60,
"description": "Let y be the remainder when d + 202 is divided by 74."
},
{
"variable": "x",
"dividend": 880,
"divisor": 91,
"remainder": 61,
"description": "Let x be the remainder when y - u + 886 is divided by 91."
},
{
"variable": "j",
"dividend": 897,
"divisor": 79,
"remainder": 28,
"description": "Let j be the remainder when x + 836 is divided by 79."
}
],
"final_dividend": 100,
"final_remainder": 23,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let x be the remainder when 187 is divided by 20. Let f be the remainder when 935 is divided by 72. Let l be the remainder when 884 is divided by 78. Let t be the remainder when x - f - l + 406 is divided by 26. Let r be the remainder when t + 301 is divided by 98. Let c be the remainder when t + 783 is divided by 61. Let z be the remainder when t + 625 is divided by 66. Let o be the remainder when c - z + r + 671 is divided by 25. Let h be the remainder when o + 323 is divided by 85. Let d be the remainder when h + 754 is divided by 19. What is the remainder when d + 153 is divided by 90?
Please reason step by step, and put your final answer within \boxed{}.
|
70
| 3
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2, 3 -> 4 -> 5, 6, 7 -> 8 -> 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "x",
"dividend": 187,
"divisor": 20,
"remainder": 7,
"description": "Let x be the remainder when 187 is divided by 20."
},
{
"variable": "f",
"dividend": 935,
"divisor": 72,
"remainder": 71,
"description": "Let f be the remainder when 935 is divided by 72."
},
{
"variable": "l",
"dividend": 884,
"divisor": 78,
"remainder": 26,
"description": "Let l be the remainder when 884 is divided by 78."
},
{
"variable": "t",
"dividend": 316,
"divisor": 26,
"remainder": 4,
"description": "Let t be the remainder when x - f - l + 406 is divided by 26."
},
{
"variable": "r",
"dividend": 305,
"divisor": 98,
"remainder": 11,
"description": "Let r be the remainder when t + 301 is divided by 98."
},
{
"variable": "c",
"dividend": 787,
"divisor": 61,
"remainder": 55,
"description": "Let c be the remainder when t + 783 is divided by 61."
},
{
"variable": "z",
"dividend": 629,
"divisor": 66,
"remainder": 35,
"description": "Let z be the remainder when t + 625 is divided by 66."
},
{
"variable": "o",
"dividend": 702,
"divisor": 25,
"remainder": 2,
"description": "Let o be the remainder when c - z + r + 671 is divided by 25."
},
{
"variable": "h",
"dividend": 325,
"divisor": 85,
"remainder": 70,
"description": "Let h be the remainder when o + 323 is divided by 85."
},
{
"variable": "d",
"dividend": 824,
"divisor": 19,
"remainder": 7,
"description": "Let d be the remainder when h + 754 is divided by 19."
}
],
"final_dividend": 160,
"final_remainder": 70,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let a be the remainder when 840 is divided by 26. Let m be the remainder when a + 576 is divided by 83. Let b be the remainder when m + 923 is divided by 70. Let g be the remainder when b + 180 is divided by 34. Let h be the remainder when b + 525 is divided by 94. Let y be the remainder when h - g + 744 is divided by 64. Let t be the remainder when y + 491 is divided by 17. Let x be the remainder when y + 333 is divided by 23. Let u be the remainder when y + 628 is divided by 34. Let f be the remainder when x - t - u + 991 is divided by 27. What is the remainder when f + 530 is divided by 19?
Please reason step by step, and put your final answer within \boxed{}.
|
2
| 4
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3 -> 4, 5 -> 6 -> 7, 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "a",
"dividend": 840,
"divisor": 26,
"remainder": 8,
"description": "Let a be the remainder when 840 is divided by 26."
},
{
"variable": "m",
"dividend": 584,
"divisor": 83,
"remainder": 3,
"description": "Let m be the remainder when a + 576 is divided by 83."
},
{
"variable": "b",
"dividend": 926,
"divisor": 70,
"remainder": 16,
"description": "Let b be the remainder when m + 923 is divided by 70."
},
{
"variable": "g",
"dividend": 196,
"divisor": 34,
"remainder": 26,
"description": "Let g be the remainder when b + 180 is divided by 34."
},
{
"variable": "h",
"dividend": 541,
"divisor": 94,
"remainder": 71,
"description": "Let h be the remainder when b + 525 is divided by 94."
},
{
"variable": "y",
"dividend": 789,
"divisor": 64,
"remainder": 21,
"description": "Let y be the remainder when h - g + 744 is divided by 64."
},
{
"variable": "t",
"dividend": 512,
"divisor": 17,
"remainder": 2,
"description": "Let t be the remainder when y + 491 is divided by 17."
},
{
"variable": "x",
"dividend": 354,
"divisor": 23,
"remainder": 9,
"description": "Let x be the remainder when y + 333 is divided by 23."
},
{
"variable": "u",
"dividend": 649,
"divisor": 34,
"remainder": 3,
"description": "Let u be the remainder when y + 628 is divided by 34."
},
{
"variable": "f",
"dividend": 995,
"divisor": 27,
"remainder": 23,
"description": "Let f be the remainder when x - t - u + 991 is divided by 27."
}
],
"final_dividend": 553,
"final_remainder": 2,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let k be the remainder when 160 is divided by 61. Let t be the remainder when k + 64 is divided by 58. Let g be the remainder when t + 858 is divided by 43. Let a be the remainder when g + 491 is divided by 46. Let o be the remainder when a + 808 is divided by 94. Let m be the remainder when o + 211 is divided by 29. Let y be the remainder when m + 155 is divided by 37. Let s be the remainder when m + 861 is divided by 17. Let w be the remainder when m + 147 is divided by 17. Let f be the remainder when m + 969 is divided by 74. What is the remainder when f + w + y - s + 200 is divided by 77?
Please reason step by step, and put your final answer within \boxed{}.
|
68
| 5
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7, 8, 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "k",
"dividend": 160,
"divisor": 61,
"remainder": 38,
"description": "Let k be the remainder when 160 is divided by 61."
},
{
"variable": "t",
"dividend": 102,
"divisor": 58,
"remainder": 44,
"description": "Let t be the remainder when k + 64 is divided by 58."
},
{
"variable": "g",
"dividend": 902,
"divisor": 43,
"remainder": 42,
"description": "Let g be the remainder when t + 858 is divided by 43."
},
{
"variable": "a",
"dividend": 533,
"divisor": 46,
"remainder": 27,
"description": "Let a be the remainder when g + 491 is divided by 46."
},
{
"variable": "o",
"dividend": 835,
"divisor": 94,
"remainder": 83,
"description": "Let o be the remainder when a + 808 is divided by 94."
},
{
"variable": "m",
"dividend": 294,
"divisor": 29,
"remainder": 4,
"description": "Let m be the remainder when o + 211 is divided by 29."
},
{
"variable": "y",
"dividend": 159,
"divisor": 37,
"remainder": 11,
"description": "Let y be the remainder when m + 155 is divided by 37."
},
{
"variable": "s",
"dividend": 865,
"divisor": 17,
"remainder": 15,
"description": "Let s be the remainder when m + 861 is divided by 17."
},
{
"variable": "w",
"dividend": 151,
"divisor": 17,
"remainder": 15,
"description": "Let w be the remainder when m + 147 is divided by 17."
},
{
"variable": "f",
"dividend": 973,
"divisor": 74,
"remainder": 11,
"description": "Let f be the remainder when m + 969 is divided by 74."
}
],
"final_dividend": 222,
"final_remainder": 68,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let s be the remainder when 234 is divided by 60. Let z be the remainder when s + 353 is divided by 92. Let j be the remainder when z + 830 is divided by 50. Let l be the remainder when j + 550 is divided by 11. Let n be the remainder when j + 183 is divided by 82. Let h be the remainder when j + 299 is divided by 78. Let m be the remainder when j + 216 is divided by 43. Let x be the remainder when l - h - m + n + 763 is divided by 18. Let w be the remainder when h + n + m - l + 332 is divided by 94. Let y be the remainder when x - w + 969 is divided by 53. What is the remainder when y + 182 is divided by 16?
Please reason step by step, and put your final answer within \boxed{}.
|
2
| 6
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3 -> 4, 5, 6, 7 -> 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "s",
"dividend": 234,
"divisor": 60,
"remainder": 54,
"description": "Let s be the remainder when 234 is divided by 60."
},
{
"variable": "z",
"dividend": 407,
"divisor": 92,
"remainder": 39,
"description": "Let z be the remainder when s + 353 is divided by 92."
},
{
"variable": "j",
"dividend": 869,
"divisor": 50,
"remainder": 19,
"description": "Let j be the remainder when z + 830 is divided by 50."
},
{
"variable": "l",
"dividend": 569,
"divisor": 11,
"remainder": 8,
"description": "Let l be the remainder when j + 550 is divided by 11."
},
{
"variable": "n",
"dividend": 202,
"divisor": 82,
"remainder": 38,
"description": "Let n be the remainder when j + 183 is divided by 82."
},
{
"variable": "h",
"dividend": 318,
"divisor": 78,
"remainder": 6,
"description": "Let h be the remainder when j + 299 is divided by 78."
},
{
"variable": "m",
"dividend": 235,
"divisor": 43,
"remainder": 20,
"description": "Let m be the remainder when j + 216 is divided by 43."
},
{
"variable": "x",
"dividend": 783,
"divisor": 18,
"remainder": 9,
"description": "Let x be the remainder when l - h - m + n + 763 is divided by 18."
},
{
"variable": "w",
"dividend": 388,
"divisor": 94,
"remainder": 12,
"description": "Let w be the remainder when h + n + m - l + 332 is divided by 94."
},
{
"variable": "y",
"dividend": 966,
"divisor": 53,
"remainder": 12,
"description": "Let y be the remainder when x - w + 969 is divided by 53."
}
],
"final_dividend": 194,
"final_remainder": 2,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let a be the remainder when 537 is divided by 100. Let x be the remainder when 214 is divided by 11. Let l be the remainder when 252 is divided by 98. Let r be the remainder when a - l + x + 429 is divided by 14. Let u be the remainder when r + 457 is divided by 15. Let b be the remainder when r + 346 is divided by 97. Let t be the remainder when b - u + 856 is divided by 55. Let y be the remainder when b - u + 838 is divided by 62. Let k be the remainder when t - y + 900 is divided by 95. Let q be the remainder when t - y + 298 is divided by 58. What is the remainder when q - k + 365 is divided by 68?
Please reason step by step, and put your final answer within \boxed{}.
|
56
| 7
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2, 3 -> 4 -> 5, 6 -> 7, 8 -> 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "a",
"dividend": 537,
"divisor": 100,
"remainder": 37,
"description": "Let a be the remainder when 537 is divided by 100."
},
{
"variable": "x",
"dividend": 214,
"divisor": 11,
"remainder": 5,
"description": "Let x be the remainder when 214 is divided by 11."
},
{
"variable": "l",
"dividend": 252,
"divisor": 98,
"remainder": 56,
"description": "Let l be the remainder when 252 is divided by 98."
},
{
"variable": "r",
"dividend": 415,
"divisor": 14,
"remainder": 9,
"description": "Let r be the remainder when a - l + x + 429 is divided by 14."
},
{
"variable": "u",
"dividend": 466,
"divisor": 15,
"remainder": 1,
"description": "Let u be the remainder when r + 457 is divided by 15."
},
{
"variable": "b",
"dividend": 355,
"divisor": 97,
"remainder": 64,
"description": "Let b be the remainder when r + 346 is divided by 97."
},
{
"variable": "t",
"dividend": 919,
"divisor": 55,
"remainder": 39,
"description": "Let t be the remainder when b - u + 856 is divided by 55."
},
{
"variable": "y",
"dividend": 901,
"divisor": 62,
"remainder": 33,
"description": "Let y be the remainder when b - u + 838 is divided by 62."
},
{
"variable": "k",
"dividend": 906,
"divisor": 95,
"remainder": 51,
"description": "Let k be the remainder when t - y + 900 is divided by 95."
},
{
"variable": "q",
"dividend": 304,
"divisor": 58,
"remainder": 14,
"description": "Let q be the remainder when t - y + 298 is divided by 58."
}
],
"final_dividend": 328,
"final_remainder": 56,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let o be the remainder when 439 is divided by 78. Let d be the remainder when o + 949 is divided by 24. Let p be the remainder when d + 680 is divided by 32. Let q be the remainder when d + 197 is divided by 14. Let n be the remainder when d + 439 is divided by 65. Let y be the remainder when d + 706 is divided by 65. Let m be the remainder when p - q - n + y + 669 is divided by 24. Let s be the remainder when p - n - y + q + 882 is divided by 97. Let a be the remainder when n - q - y - p + 261 is divided by 74. Let k be the remainder when n - p - q - y + 358 is divided by 95. What is the remainder when k - s - a - m + 679 is divided by 36?
Please reason step by step, and put your final answer within \boxed{}.
|
11
| 8
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3, 4, 5, 6 -> 7, 8, 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "o",
"dividend": 439,
"divisor": 78,
"remainder": 49,
"description": "Let o be the remainder when 439 is divided by 78."
},
{
"variable": "d",
"dividend": 998,
"divisor": 24,
"remainder": 14,
"description": "Let d be the remainder when o + 949 is divided by 24."
},
{
"variable": "p",
"dividend": 694,
"divisor": 32,
"remainder": 22,
"description": "Let p be the remainder when d + 680 is divided by 32."
},
{
"variable": "q",
"dividend": 211,
"divisor": 14,
"remainder": 1,
"description": "Let q be the remainder when d + 197 is divided by 14."
},
{
"variable": "n",
"dividend": 453,
"divisor": 65,
"remainder": 63,
"description": "Let n be the remainder when d + 439 is divided by 65."
},
{
"variable": "y",
"dividend": 720,
"divisor": 65,
"remainder": 5,
"description": "Let y be the remainder when d + 706 is divided by 65."
},
{
"variable": "m",
"dividend": 632,
"divisor": 24,
"remainder": 8,
"description": "Let m be the remainder when p - q - n + y + 669 is divided by 24."
},
{
"variable": "s",
"dividend": 837,
"divisor": 97,
"remainder": 61,
"description": "Let s be the remainder when p - n - y + q + 882 is divided by 97."
},
{
"variable": "a",
"dividend": 296,
"divisor": 74,
"remainder": 0,
"description": "Let a be the remainder when n - q - y - p + 261 is divided by 74."
},
{
"variable": "k",
"dividend": 393,
"divisor": 95,
"remainder": 13,
"description": "Let k be the remainder when n - p - q - y + 358 is divided by 95."
}
],
"final_dividend": 623,
"final_remainder": 11,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let k be the remainder when 125 is divided by 28. Let i be the remainder when 586 is divided by 41. Let o be the remainder when i - k + 836 is divided by 19. Let g be the remainder when o + 491 is divided by 73. Let p be the remainder when o + 753 is divided by 28. Let d be the remainder when o + 879 is divided by 23. Let b be the remainder when d - p + g + 180 is divided by 38. Let t be the remainder when b + 635 is divided by 95. Let x be the remainder when b + 719 is divided by 66. Let n be the remainder when t - x + 488 is divided by 80. What is the remainder when n + 869 is divided by 43?
Please reason step by step, and put your final answer within \boxed{}.
|
9
| 9
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2 -> 3 -> 4, 5, 6 -> 7 -> 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "k",
"dividend": 125,
"divisor": 28,
"remainder": 13,
"description": "Let k be the remainder when 125 is divided by 28."
},
{
"variable": "i",
"dividend": 586,
"divisor": 41,
"remainder": 12,
"description": "Let i be the remainder when 586 is divided by 41."
},
{
"variable": "o",
"dividend": 835,
"divisor": 19,
"remainder": 18,
"description": "Let o be the remainder when i - k + 836 is divided by 19."
},
{
"variable": "g",
"dividend": 509,
"divisor": 73,
"remainder": 71,
"description": "Let g be the remainder when o + 491 is divided by 73."
},
{
"variable": "p",
"dividend": 771,
"divisor": 28,
"remainder": 15,
"description": "Let p be the remainder when o + 753 is divided by 28."
},
{
"variable": "d",
"dividend": 897,
"divisor": 23,
"remainder": 0,
"description": "Let d be the remainder when o + 879 is divided by 23."
},
{
"variable": "b",
"dividend": 236,
"divisor": 38,
"remainder": 8,
"description": "Let b be the remainder when d - p + g + 180 is divided by 38."
},
{
"variable": "t",
"dividend": 643,
"divisor": 95,
"remainder": 73,
"description": "Let t be the remainder when b + 635 is divided by 95."
},
{
"variable": "x",
"dividend": 727,
"divisor": 66,
"remainder": 1,
"description": "Let x be the remainder when b + 719 is divided by 66."
},
{
"variable": "n",
"dividend": 560,
"divisor": 80,
"remainder": 0,
"description": "Let n be the remainder when t - x + 488 is divided by 80."
}
],
"final_dividend": 869,
"final_remainder": 9,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let s be the remainder when 427 is divided by 52. Let x be the remainder when s + 230 is divided by 20. Let v be the remainder when s + 481 is divided by 39. Let t be the remainder when s + 308 is divided by 100. Let l be the remainder when v - t - x + 307 is divided by 63. Let a be the remainder when t - x - v + 466 is divided by 59. Let z be the remainder when x - t - v + 588 is divided by 59. Let k be the remainder when z - l - a + 321 is divided by 13. Let d be the remainder when a - l + z + 984 is divided by 60. Let b be the remainder when k - d + 334 is divided by 33. What is the remainder when b + 415 is divided by 68?
Please reason step by step, and put your final answer within \boxed{}.
|
26
| 10
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2, 3, 4 -> 5, 6, 7 -> 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "s",
"dividend": 427,
"divisor": 52,
"remainder": 11,
"description": "Let s be the remainder when 427 is divided by 52."
},
{
"variable": "x",
"dividend": 241,
"divisor": 20,
"remainder": 1,
"description": "Let x be the remainder when s + 230 is divided by 20."
},
{
"variable": "v",
"dividend": 492,
"divisor": 39,
"remainder": 24,
"description": "Let v be the remainder when s + 481 is divided by 39."
},
{
"variable": "t",
"dividend": 319,
"divisor": 100,
"remainder": 19,
"description": "Let t be the remainder when s + 308 is divided by 100."
},
{
"variable": "l",
"dividend": 311,
"divisor": 63,
"remainder": 59,
"description": "Let l be the remainder when v - t - x + 307 is divided by 63."
},
{
"variable": "a",
"dividend": 460,
"divisor": 59,
"remainder": 47,
"description": "Let a be the remainder when t - x - v + 466 is divided by 59."
},
{
"variable": "z",
"dividend": 546,
"divisor": 59,
"remainder": 15,
"description": "Let z be the remainder when x - t - v + 588 is divided by 59."
},
{
"variable": "k",
"dividend": 230,
"divisor": 13,
"remainder": 9,
"description": "Let k be the remainder when z - l - a + 321 is divided by 13."
},
{
"variable": "d",
"dividend": 987,
"divisor": 60,
"remainder": 27,
"description": "Let d be the remainder when a - l + z + 984 is divided by 60."
},
{
"variable": "b",
"dividend": 316,
"divisor": 33,
"remainder": 19,
"description": "Let b be the remainder when k - d + 334 is divided by 33."
}
],
"final_dividend": 434,
"final_remainder": 26,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let c be the remainder when 765 is divided by 38. Let l be the remainder when 141 is divided by 93. Let d be the remainder when 304 is divided by 41. Let i be the remainder when 256 is divided by 89. Let q be the remainder when 584 is divided by 26. Let k be the remainder when 323 is divided by 82. Let w be the remainder when i - c + q + l - k - d + 467 is divided by 99. Let v be the remainder when i + k - d - c - l + q + 8 is divided by 19. Let p be the remainder when w - v + 469 is divided by 63. Let f be the remainder when p + 227 is divided by 100. What is the remainder when f + 224 is divided by 65?
Please reason step by step, and put your final answer within \boxed{}.
|
20
| 11
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2, 3, 4, 5, 6 -> 7, 8 -> 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "c",
"dividend": 765,
"divisor": 38,
"remainder": 5,
"description": "Let c be the remainder when 765 is divided by 38."
},
{
"variable": "l",
"dividend": 141,
"divisor": 93,
"remainder": 48,
"description": "Let l be the remainder when 141 is divided by 93."
},
{
"variable": "d",
"dividend": 304,
"divisor": 41,
"remainder": 17,
"description": "Let d be the remainder when 304 is divided by 41."
},
{
"variable": "i",
"dividend": 256,
"divisor": 89,
"remainder": 78,
"description": "Let i be the remainder when 256 is divided by 89."
},
{
"variable": "q",
"dividend": 584,
"divisor": 26,
"remainder": 12,
"description": "Let q be the remainder when 584 is divided by 26."
},
{
"variable": "k",
"dividend": 323,
"divisor": 82,
"remainder": 77,
"description": "Let k be the remainder when 323 is divided by 82."
},
{
"variable": "w",
"dividend": 506,
"divisor": 99,
"remainder": 11,
"description": "Let w be the remainder when i - c + q + l - k - d + 467 is divided by 99."
},
{
"variable": "v",
"dividend": 105,
"divisor": 19,
"remainder": 10,
"description": "Let v be the remainder when i + k - d - c - l + q + 8 is divided by 19."
},
{
"variable": "p",
"dividend": 470,
"divisor": 63,
"remainder": 29,
"description": "Let p be the remainder when w - v + 469 is divided by 63."
},
{
"variable": "f",
"dividend": 256,
"divisor": 100,
"remainder": 56,
"description": "Let f be the remainder when p + 227 is divided by 100."
}
],
"final_dividend": 280,
"final_remainder": 20,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let g be the remainder when 868 is divided by 41. Let j be the remainder when 724 is divided by 82. Let n be the remainder when 444 is divided by 58. Let d be the remainder when 971 is divided by 73. Let c be the remainder when 599 is divided by 33. Let b be the remainder when 916 is divided by 55. Let y be the remainder when 386 is divided by 53. Let a be the remainder when b - n - d - y - j + c + g + 496 is divided by 81. Let w be the remainder when a + 731 is divided by 61. Let x be the remainder when a + 702 is divided by 49. What is the remainder when x - w + 834 is divided by 84?
Please reason step by step, and put your final answer within \boxed{}.
|
23
| 12
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2, 3, 4, 5, 6, 7 -> 8 -> 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "g",
"dividend": 868,
"divisor": 41,
"remainder": 7,
"description": "Let g be the remainder when 868 is divided by 41."
},
{
"variable": "j",
"dividend": 724,
"divisor": 82,
"remainder": 68,
"description": "Let j be the remainder when 724 is divided by 82."
},
{
"variable": "n",
"dividend": 444,
"divisor": 58,
"remainder": 38,
"description": "Let n be the remainder when 444 is divided by 58."
},
{
"variable": "d",
"dividend": 971,
"divisor": 73,
"remainder": 22,
"description": "Let d be the remainder when 971 is divided by 73."
},
{
"variable": "c",
"dividend": 599,
"divisor": 33,
"remainder": 5,
"description": "Let c be the remainder when 599 is divided by 33."
},
{
"variable": "b",
"dividend": 916,
"divisor": 55,
"remainder": 36,
"description": "Let b be the remainder when 916 is divided by 55."
},
{
"variable": "y",
"dividend": 386,
"divisor": 53,
"remainder": 15,
"description": "Let y be the remainder when 386 is divided by 53."
},
{
"variable": "a",
"dividend": 401,
"divisor": 81,
"remainder": 77,
"description": "Let a be the remainder when b - n - d - y - j + c + g + 496 is divided by 81."
},
{
"variable": "w",
"dividend": 808,
"divisor": 61,
"remainder": 15,
"description": "Let w be the remainder when a + 731 is divided by 61."
},
{
"variable": "x",
"dividend": 779,
"divisor": 49,
"remainder": 44,
"description": "Let x be the remainder when a + 702 is divided by 49."
}
],
"final_dividend": 863,
"final_remainder": 23,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let q be the remainder when 860 is divided by 25. Let x be the remainder when 289 is divided by 98. Let k be the remainder when 856 is divided by 37. Let a be the remainder when 841 is divided by 45. Let z be the remainder when 711 is divided by 77. Let c be the remainder when 952 is divided by 22. Let p be the remainder when 332 is divided by 47. Let m be the remainder when p - c + a - x + z + q - k + 622 is divided by 32. Let f be the remainder when m + 444 is divided by 66. Let g be the remainder when f + 306 is divided by 16. What is the remainder when g + 210 is divided by 71?
Please reason step by step, and put your final answer within \boxed{}.
|
3
| 13
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2, 3, 4, 5, 6, 7 -> 8 -> 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "q",
"dividend": 860,
"divisor": 25,
"remainder": 10,
"description": "Let q be the remainder when 860 is divided by 25."
},
{
"variable": "x",
"dividend": 289,
"divisor": 98,
"remainder": 93,
"description": "Let x be the remainder when 289 is divided by 98."
},
{
"variable": "k",
"dividend": 856,
"divisor": 37,
"remainder": 5,
"description": "Let k be the remainder when 856 is divided by 37."
},
{
"variable": "a",
"dividend": 841,
"divisor": 45,
"remainder": 31,
"description": "Let a be the remainder when 841 is divided by 45."
},
{
"variable": "z",
"dividend": 711,
"divisor": 77,
"remainder": 18,
"description": "Let z be the remainder when 711 is divided by 77."
},
{
"variable": "c",
"dividend": 952,
"divisor": 22,
"remainder": 6,
"description": "Let c be the remainder when 952 is divided by 22."
},
{
"variable": "p",
"dividend": 332,
"divisor": 47,
"remainder": 3,
"description": "Let p be the remainder when 332 is divided by 47."
},
{
"variable": "m",
"dividend": 580,
"divisor": 32,
"remainder": 4,
"description": "Let m be the remainder when p - c + a - x + z + q - k + 622 is divided by 32."
},
{
"variable": "f",
"dividend": 448,
"divisor": 66,
"remainder": 52,
"description": "Let f be the remainder when m + 444 is divided by 66."
},
{
"variable": "g",
"dividend": 358,
"divisor": 16,
"remainder": 6,
"description": "Let g be the remainder when f + 306 is divided by 16."
}
],
"final_dividend": 216,
"final_remainder": 3,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let b be the remainder when 671 is divided by 25. Let g be the remainder when b + 689 is divided by 87. Let o be the remainder when b + 873 is divided by 38. Let x be the remainder when b + 540 is divided by 58. Let w be the remainder when o - g + x + 836 is divided by 48. Let k be the remainder when w + 299 is divided by 90. Let c be the remainder when k + 137 is divided by 94. Let u be the remainder when c + 188 is divided by 40. Let i be the remainder when c + 13 is divided by 30. Let n be the remainder when i - u + 362 is divided by 67. What is the remainder when n + 821 is divided by 46?
Please reason step by step, and put your final answer within \boxed{}.
|
41
| 14
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2, 3, 4 -> 5 -> 6 -> 7 -> 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "b",
"dividend": 671,
"divisor": 25,
"remainder": 21,
"description": "Let b be the remainder when 671 is divided by 25."
},
{
"variable": "g",
"dividend": 710,
"divisor": 87,
"remainder": 14,
"description": "Let g be the remainder when b + 689 is divided by 87."
},
{
"variable": "o",
"dividend": 894,
"divisor": 38,
"remainder": 20,
"description": "Let o be the remainder when b + 873 is divided by 38."
},
{
"variable": "x",
"dividend": 561,
"divisor": 58,
"remainder": 39,
"description": "Let x be the remainder when b + 540 is divided by 58."
},
{
"variable": "w",
"dividend": 881,
"divisor": 48,
"remainder": 17,
"description": "Let w be the remainder when o - g + x + 836 is divided by 48."
},
{
"variable": "k",
"dividend": 316,
"divisor": 90,
"remainder": 46,
"description": "Let k be the remainder when w + 299 is divided by 90."
},
{
"variable": "c",
"dividend": 183,
"divisor": 94,
"remainder": 89,
"description": "Let c be the remainder when k + 137 is divided by 94."
},
{
"variable": "u",
"dividend": 277,
"divisor": 40,
"remainder": 37,
"description": "Let u be the remainder when c + 188 is divided by 40."
},
{
"variable": "i",
"dividend": 102,
"divisor": 30,
"remainder": 12,
"description": "Let i be the remainder when c + 13 is divided by 30."
},
{
"variable": "n",
"dividend": 337,
"divisor": 67,
"remainder": 2,
"description": "Let n be the remainder when i - u + 362 is divided by 67."
}
],
"final_dividend": 823,
"final_remainder": 41,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let r be the remainder when 372 is divided by 29. Let v be the remainder when 161 is divided by 19. Let k be the remainder when 709 is divided by 49. Let o be the remainder when r - k - v + 620 is divided by 46. Let m be the remainder when o + 534 is divided by 73. Let l be the remainder when o + 126 is divided by 86. Let d be the remainder when l - m + 773 is divided by 51. Let p be the remainder when m - l + 648 is divided by 96. Let b be the remainder when p - d + 551 is divided by 45. Let z be the remainder when b + 400 is divided by 62. What is the remainder when z + 779 is divided by 51?
Please reason step by step, and put your final answer within \boxed{}.
|
21
| 15
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2, 3 -> 4 -> 5, 6 -> 7, 8 -> 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "r",
"dividend": 372,
"divisor": 29,
"remainder": 24,
"description": "Let r be the remainder when 372 is divided by 29."
},
{
"variable": "v",
"dividend": 161,
"divisor": 19,
"remainder": 9,
"description": "Let v be the remainder when 161 is divided by 19."
},
{
"variable": "k",
"dividend": 709,
"divisor": 49,
"remainder": 23,
"description": "Let k be the remainder when 709 is divided by 49."
},
{
"variable": "o",
"dividend": 612,
"divisor": 46,
"remainder": 14,
"description": "Let o be the remainder when r - k - v + 620 is divided by 46."
},
{
"variable": "m",
"dividend": 548,
"divisor": 73,
"remainder": 37,
"description": "Let m be the remainder when o + 534 is divided by 73."
},
{
"variable": "l",
"dividend": 140,
"divisor": 86,
"remainder": 54,
"description": "Let l be the remainder when o + 126 is divided by 86."
},
{
"variable": "d",
"dividend": 790,
"divisor": 51,
"remainder": 25,
"description": "Let d be the remainder when l - m + 773 is divided by 51."
},
{
"variable": "p",
"dividend": 631,
"divisor": 96,
"remainder": 55,
"description": "Let p be the remainder when m - l + 648 is divided by 96."
},
{
"variable": "b",
"dividend": 581,
"divisor": 45,
"remainder": 41,
"description": "Let b be the remainder when p - d + 551 is divided by 45."
},
{
"variable": "z",
"dividend": 441,
"divisor": 62,
"remainder": 7,
"description": "Let z be the remainder when b + 400 is divided by 62."
}
],
"final_dividend": 786,
"final_remainder": 21,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let l be the remainder when 358 is divided by 50. Let c be the remainder when l + 883 is divided by 24. Let g be the remainder when c + 941 is divided by 75. Let d be the remainder when c + 987 is divided by 94. Let o be the remainder when c + 520 is divided by 69. Let h be the remainder when c + 627 is divided by 34. Let z be the remainder when c + 871 is divided by 89. Let b be the remainder when c + 549 is divided by 90. Let q be the remainder when b - g + h + d + z - o + 595 is divided by 36. Let p be the remainder when o + b - z - d - g - h + 1087 is divided by 80. What is the remainder when q - p + 722 is divided by 71?
Please reason step by step, and put your final answer within \boxed{}.
|
25
| 16
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3, 4, 5, 6, 7, 8 -> 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "l",
"dividend": 358,
"divisor": 50,
"remainder": 8,
"description": "Let l be the remainder when 358 is divided by 50."
},
{
"variable": "c",
"dividend": 891,
"divisor": 24,
"remainder": 3,
"description": "Let c be the remainder when l + 883 is divided by 24."
},
{
"variable": "g",
"dividend": 944,
"divisor": 75,
"remainder": 44,
"description": "Let g be the remainder when c + 941 is divided by 75."
},
{
"variable": "d",
"dividend": 990,
"divisor": 94,
"remainder": 50,
"description": "Let d be the remainder when c + 987 is divided by 94."
},
{
"variable": "o",
"dividend": 523,
"divisor": 69,
"remainder": 40,
"description": "Let o be the remainder when c + 520 is divided by 69."
},
{
"variable": "h",
"dividend": 630,
"divisor": 34,
"remainder": 18,
"description": "Let h be the remainder when c + 627 is divided by 34."
},
{
"variable": "z",
"dividend": 874,
"divisor": 89,
"remainder": 73,
"description": "Let z be the remainder when c + 871 is divided by 89."
},
{
"variable": "b",
"dividend": 552,
"divisor": 90,
"remainder": 12,
"description": "Let b be the remainder when c + 549 is divided by 90."
},
{
"variable": "q",
"dividend": 664,
"divisor": 36,
"remainder": 16,
"description": "Let q be the remainder when b - g + h + d + z - o + 595 is divided by 36."
},
{
"variable": "p",
"dividend": 954,
"divisor": 80,
"remainder": 74,
"description": "Let p be the remainder when o + b - z - d - g - h + 1087 is divided by 80."
}
],
"final_dividend": 664,
"final_remainder": 25,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let d be the remainder when 843 is divided by 46. Let q be the remainder when d + 678 is divided by 85. Let n be the remainder when d + 971 is divided by 72. Let t be the remainder when n - q + 529 is divided by 67. Let y be the remainder when t + 784 is divided by 34. Let p be the remainder when y + 460 is divided by 83. Let j be the remainder when y + 112 is divided by 62. Let m be the remainder when y + 790 is divided by 70. Let z be the remainder when y + 747 is divided by 59. Let u be the remainder when y + 105 is divided by 73. What is the remainder when z - j + p + m - u + 934 is divided by 26?
Please reason step by step, and put your final answer within \boxed{}.
|
3
| 17
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2, 3 -> 4 -> 5 -> 6, 7, 8, 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "d",
"dividend": 843,
"divisor": 46,
"remainder": 15,
"description": "Let d be the remainder when 843 is divided by 46."
},
{
"variable": "q",
"dividend": 693,
"divisor": 85,
"remainder": 13,
"description": "Let q be the remainder when d + 678 is divided by 85."
},
{
"variable": "n",
"dividend": 986,
"divisor": 72,
"remainder": 50,
"description": "Let n be the remainder when d + 971 is divided by 72."
},
{
"variable": "t",
"dividend": 566,
"divisor": 67,
"remainder": 30,
"description": "Let t be the remainder when n - q + 529 is divided by 67."
},
{
"variable": "y",
"dividend": 814,
"divisor": 34,
"remainder": 32,
"description": "Let y be the remainder when t + 784 is divided by 34."
},
{
"variable": "p",
"dividend": 492,
"divisor": 83,
"remainder": 77,
"description": "Let p be the remainder when y + 460 is divided by 83."
},
{
"variable": "j",
"dividend": 144,
"divisor": 62,
"remainder": 20,
"description": "Let j be the remainder when y + 112 is divided by 62."
},
{
"variable": "m",
"dividend": 822,
"divisor": 70,
"remainder": 52,
"description": "Let m be the remainder when y + 790 is divided by 70."
},
{
"variable": "z",
"dividend": 779,
"divisor": 59,
"remainder": 12,
"description": "Let z be the remainder when y + 747 is divided by 59."
},
{
"variable": "u",
"dividend": 137,
"divisor": 73,
"remainder": 64,
"description": "Let u be the remainder when y + 105 is divided by 73."
}
],
"final_dividend": 991,
"final_remainder": 3,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let q be the remainder when 835 is divided by 90. Let w be the remainder when q + 111 is divided by 79. Let o be the remainder when w + 283 is divided by 18. Let n be the remainder when w + 337 is divided by 97. Let b be the remainder when w + 487 is divided by 21. Let h be the remainder when w + 763 is divided by 91. Let t be the remainder when w + 213 is divided by 66. Let v be the remainder when b - n - t - h + o + 621 is divided by 13. Let z be the remainder when b - h - o + t + n + 558 is divided by 82. Let j be the remainder when h + t - n - o - b + 788 is divided by 68. What is the remainder when j - z - v + 573 is divided by 64?
Please reason step by step, and put your final answer within \boxed{}.
|
45
| 18
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3, 4, 5, 6, 7 -> 8, 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "q",
"dividend": 835,
"divisor": 90,
"remainder": 25,
"description": "Let q be the remainder when 835 is divided by 90."
},
{
"variable": "w",
"dividend": 136,
"divisor": 79,
"remainder": 57,
"description": "Let w be the remainder when q + 111 is divided by 79."
},
{
"variable": "o",
"dividend": 340,
"divisor": 18,
"remainder": 16,
"description": "Let o be the remainder when w + 283 is divided by 18."
},
{
"variable": "n",
"dividend": 394,
"divisor": 97,
"remainder": 6,
"description": "Let n be the remainder when w + 337 is divided by 97."
},
{
"variable": "b",
"dividend": 544,
"divisor": 21,
"remainder": 19,
"description": "Let b be the remainder when w + 487 is divided by 21."
},
{
"variable": "h",
"dividend": 820,
"divisor": 91,
"remainder": 1,
"description": "Let h be the remainder when w + 763 is divided by 91."
},
{
"variable": "t",
"dividend": 270,
"divisor": 66,
"remainder": 6,
"description": "Let t be the remainder when w + 213 is divided by 66."
},
{
"variable": "v",
"dividend": 643,
"divisor": 13,
"remainder": 6,
"description": "Let v be the remainder when b - n - t - h + o + 621 is divided by 13."
},
{
"variable": "z",
"dividend": 572,
"divisor": 82,
"remainder": 80,
"description": "Let z be the remainder when b - h - o + t + n + 558 is divided by 82."
},
{
"variable": "j",
"dividend": 754,
"divisor": 68,
"remainder": 6,
"description": "Let j be the remainder when h + t - n - o - b + 788 is divided by 68."
}
],
"final_dividend": 493,
"final_remainder": 45,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let s be the remainder when 679 is divided by 11. Let z be the remainder when 720 is divided by 16. Let w be the remainder when s - z + 743 is divided by 46. Let k be the remainder when w + 341 is divided by 89. Let v be the remainder when w + 184 is divided by 90. Let i be the remainder when w + 892 is divided by 49. Let g be the remainder when w + 678 is divided by 14. Let m be the remainder when w + 177 is divided by 26. Let a be the remainder when k - i - m - v - g + 986 is divided by 51. Let x be the remainder when v - i - m + g - k + 123 is divided by 53. What is the remainder when a - x + 699 is divided by 43?
Please reason step by step, and put your final answer within \boxed{}.
|
10
| 19
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2 -> 3 -> 4, 5, 6, 7, 8 -> 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "s",
"dividend": 679,
"divisor": 11,
"remainder": 8,
"description": "Let s be the remainder when 679 is divided by 11."
},
{
"variable": "z",
"dividend": 720,
"divisor": 16,
"remainder": 0,
"description": "Let z be the remainder when 720 is divided by 16."
},
{
"variable": "w",
"dividend": 751,
"divisor": 46,
"remainder": 15,
"description": "Let w be the remainder when s - z + 743 is divided by 46."
},
{
"variable": "k",
"dividend": 356,
"divisor": 89,
"remainder": 0,
"description": "Let k be the remainder when w + 341 is divided by 89."
},
{
"variable": "v",
"dividend": 199,
"divisor": 90,
"remainder": 19,
"description": "Let v be the remainder when w + 184 is divided by 90."
},
{
"variable": "i",
"dividend": 907,
"divisor": 49,
"remainder": 25,
"description": "Let i be the remainder when w + 892 is divided by 49."
},
{
"variable": "g",
"dividend": 693,
"divisor": 14,
"remainder": 7,
"description": "Let g be the remainder when w + 678 is divided by 14."
},
{
"variable": "m",
"dividend": 192,
"divisor": 26,
"remainder": 10,
"description": "Let m be the remainder when w + 177 is divided by 26."
},
{
"variable": "a",
"dividend": 925,
"divisor": 51,
"remainder": 7,
"description": "Let a be the remainder when k - i - m - v - g + 986 is divided by 51."
},
{
"variable": "x",
"dividend": 114,
"divisor": 53,
"remainder": 8,
"description": "Let x be the remainder when v - i - m + g - k + 123 is divided by 53."
}
],
"final_dividend": 698,
"final_remainder": 10,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let r be the remainder when 817 is divided by 69. Let p be the remainder when 518 is divided by 93. Let h be the remainder when 146 is divided by 27. Let i be the remainder when h - r + p + 558 is divided by 48. Let g be the remainder when i + 824 is divided by 95. Let z be the remainder when i + 665 is divided by 63. Let y be the remainder when g - z + 136 is divided by 63. Let n be the remainder when z - g + 972 is divided by 37. Let o be the remainder when n - y + 501 is divided by 22. Let a be the remainder when o + 224 is divided by 34. What is the remainder when a + 172 is divided by 68?
Please reason step by step, and put your final answer within \boxed{}.
|
57
| 20
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2, 3 -> 4 -> 5, 6 -> 7, 8 -> 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "r",
"dividend": 817,
"divisor": 69,
"remainder": 58,
"description": "Let r be the remainder when 817 is divided by 69."
},
{
"variable": "p",
"dividend": 518,
"divisor": 93,
"remainder": 53,
"description": "Let p be the remainder when 518 is divided by 93."
},
{
"variable": "h",
"dividend": 146,
"divisor": 27,
"remainder": 11,
"description": "Let h be the remainder when 146 is divided by 27."
},
{
"variable": "i",
"dividend": 564,
"divisor": 48,
"remainder": 36,
"description": "Let i be the remainder when h - r + p + 558 is divided by 48."
},
{
"variable": "g",
"dividend": 860,
"divisor": 95,
"remainder": 5,
"description": "Let g be the remainder when i + 824 is divided by 95."
},
{
"variable": "z",
"dividend": 701,
"divisor": 63,
"remainder": 8,
"description": "Let z be the remainder when i + 665 is divided by 63."
},
{
"variable": "y",
"dividend": 133,
"divisor": 63,
"remainder": 7,
"description": "Let y be the remainder when g - z + 136 is divided by 63."
},
{
"variable": "n",
"dividend": 975,
"divisor": 37,
"remainder": 13,
"description": "Let n be the remainder when z - g + 972 is divided by 37."
},
{
"variable": "o",
"dividend": 507,
"divisor": 22,
"remainder": 1,
"description": "Let o be the remainder when n - y + 501 is divided by 22."
},
{
"variable": "a",
"dividend": 225,
"divisor": 34,
"remainder": 21,
"description": "Let a be the remainder when o + 224 is divided by 34."
}
],
"final_dividend": 193,
"final_remainder": 57,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let x be the remainder when 932 is divided by 37. Let b be the remainder when x + 885 is divided by 52. Let v be the remainder when b + 94 is divided by 86. Let q be the remainder when v + 217 is divided by 28. Let o be the remainder when v + 901 is divided by 42. Let k be the remainder when o - q + 882 is divided by 24. Let c be the remainder when k + 411 is divided by 85. Let d be the remainder when c + 365 is divided by 32. Let y be the remainder when d + 840 is divided by 26. Let n be the remainder when y + 215 is divided by 77. What is the remainder when n + 525 is divided by 18?
Please reason step by step, and put your final answer within \boxed{}.
|
11
| 21
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3 -> 4, 5 -> 6 -> 7 -> 8 -> 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "x",
"dividend": 932,
"divisor": 37,
"remainder": 7,
"description": "Let x be the remainder when 932 is divided by 37."
},
{
"variable": "b",
"dividend": 892,
"divisor": 52,
"remainder": 8,
"description": "Let b be the remainder when x + 885 is divided by 52."
},
{
"variable": "v",
"dividend": 102,
"divisor": 86,
"remainder": 16,
"description": "Let v be the remainder when b + 94 is divided by 86."
},
{
"variable": "q",
"dividend": 233,
"divisor": 28,
"remainder": 9,
"description": "Let q be the remainder when v + 217 is divided by 28."
},
{
"variable": "o",
"dividend": 917,
"divisor": 42,
"remainder": 35,
"description": "Let o be the remainder when v + 901 is divided by 42."
},
{
"variable": "k",
"dividend": 908,
"divisor": 24,
"remainder": 20,
"description": "Let k be the remainder when o - q + 882 is divided by 24."
},
{
"variable": "c",
"dividend": 431,
"divisor": 85,
"remainder": 6,
"description": "Let c be the remainder when k + 411 is divided by 85."
},
{
"variable": "d",
"dividend": 371,
"divisor": 32,
"remainder": 19,
"description": "Let d be the remainder when c + 365 is divided by 32."
},
{
"variable": "y",
"dividend": 859,
"divisor": 26,
"remainder": 1,
"description": "Let y be the remainder when d + 840 is divided by 26."
},
{
"variable": "n",
"dividend": 216,
"divisor": 77,
"remainder": 62,
"description": "Let n be the remainder when y + 215 is divided by 77."
}
],
"final_dividend": 587,
"final_remainder": 11,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let i be the remainder when 967 is divided by 71. Let y be the remainder when 802 is divided by 64. Let v be the remainder when 829 is divided by 72. Let a be the remainder when v - y + i + 692 is divided by 19. Let f be the remainder when v - y - i + 760 is divided by 84. Let w be the remainder when f - a + 532 is divided by 22. Let u be the remainder when w + 435 is divided by 62. Let t be the remainder when w + 513 is divided by 61. Let l be the remainder when w + 525 is divided by 50. Let r be the remainder when u - l + t + 180 is divided by 95. What is the remainder when r + 192 is divided by 20?
Please reason step by step, and put your final answer within \boxed{}.
|
15
| 22
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2, 3 -> 4, 5 -> 6 -> 7, 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "i",
"dividend": 967,
"divisor": 71,
"remainder": 44,
"description": "Let i be the remainder when 967 is divided by 71."
},
{
"variable": "y",
"dividend": 802,
"divisor": 64,
"remainder": 34,
"description": "Let y be the remainder when 802 is divided by 64."
},
{
"variable": "v",
"dividend": 829,
"divisor": 72,
"remainder": 37,
"description": "Let v be the remainder when 829 is divided by 72."
},
{
"variable": "a",
"dividend": 739,
"divisor": 19,
"remainder": 17,
"description": "Let a be the remainder when v - y + i + 692 is divided by 19."
},
{
"variable": "f",
"dividend": 719,
"divisor": 84,
"remainder": 47,
"description": "Let f be the remainder when v - y - i + 760 is divided by 84."
},
{
"variable": "w",
"dividend": 562,
"divisor": 22,
"remainder": 12,
"description": "Let w be the remainder when f - a + 532 is divided by 22."
},
{
"variable": "u",
"dividend": 447,
"divisor": 62,
"remainder": 13,
"description": "Let u be the remainder when w + 435 is divided by 62."
},
{
"variable": "t",
"dividend": 525,
"divisor": 61,
"remainder": 37,
"description": "Let t be the remainder when w + 513 is divided by 61."
},
{
"variable": "l",
"dividend": 537,
"divisor": 50,
"remainder": 37,
"description": "Let l be the remainder when w + 525 is divided by 50."
},
{
"variable": "r",
"dividend": 193,
"divisor": 95,
"remainder": 3,
"description": "Let r be the remainder when u - l + t + 180 is divided by 95."
}
],
"final_dividend": 195,
"final_remainder": 15,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let o be the remainder when 988 is divided by 64. Let f be the remainder when 394 is divided by 16. Let m be the remainder when f - o + 790 is divided by 49. Let j be the remainder when f - o + 898 is divided by 38. Let s be the remainder when m - j + 692 is divided by 83. Let p be the remainder when s + 225 is divided by 13. Let u be the remainder when s + 821 is divided by 99. Let w be the remainder when u - p + 602 is divided by 53. Let n be the remainder when p - u + 562 is divided by 18. Let t be the remainder when p - u + 496 is divided by 68. What is the remainder when n + w - t + 101 is divided by 51?
Please reason step by step, and put your final answer within \boxed{}.
|
48
| 23
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2 -> 3, 4 -> 5 -> 6, 7 -> 8, 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "o",
"dividend": 988,
"divisor": 64,
"remainder": 28,
"description": "Let o be the remainder when 988 is divided by 64."
},
{
"variable": "f",
"dividend": 394,
"divisor": 16,
"remainder": 10,
"description": "Let f be the remainder when 394 is divided by 16."
},
{
"variable": "m",
"dividend": 772,
"divisor": 49,
"remainder": 37,
"description": "Let m be the remainder when f - o + 790 is divided by 49."
},
{
"variable": "j",
"dividend": 880,
"divisor": 38,
"remainder": 6,
"description": "Let j be the remainder when f - o + 898 is divided by 38."
},
{
"variable": "s",
"dividend": 723,
"divisor": 83,
"remainder": 59,
"description": "Let s be the remainder when m - j + 692 is divided by 83."
},
{
"variable": "p",
"dividend": 284,
"divisor": 13,
"remainder": 11,
"description": "Let p be the remainder when s + 225 is divided by 13."
},
{
"variable": "u",
"dividend": 880,
"divisor": 99,
"remainder": 88,
"description": "Let u be the remainder when s + 821 is divided by 99."
},
{
"variable": "w",
"dividend": 679,
"divisor": 53,
"remainder": 43,
"description": "Let w be the remainder when u - p + 602 is divided by 53."
},
{
"variable": "n",
"dividend": 485,
"divisor": 18,
"remainder": 17,
"description": "Let n be the remainder when p - u + 562 is divided by 18."
},
{
"variable": "t",
"dividend": 419,
"divisor": 68,
"remainder": 11,
"description": "Let t be the remainder when p - u + 496 is divided by 68."
}
],
"final_dividend": 150,
"final_remainder": 48,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let f be the remainder when 216 is divided by 75. Let c be the remainder when f + 147 is divided by 65. Let p be the remainder when f + 728 is divided by 96. Let r be the remainder when f + 573 is divided by 72. Let q be the remainder when f + 259 is divided by 15. Let j be the remainder when f + 90 is divided by 86. Let i be the remainder when f + 342 is divided by 36. Let v be the remainder when f + 816 is divided by 27. Let x be the remainder when f + 369 is divided by 47. Let l be the remainder when c - r - v + j - p + q - i + x + 991 is divided by 10. What is the remainder when l + 687 is divided by 50?
Please reason step by step, and put your final answer within \boxed{}.
|
39
| 24
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2, 3, 4, 5, 6, 7, 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "f",
"dividend": 216,
"divisor": 75,
"remainder": 66,
"description": "Let f be the remainder when 216 is divided by 75."
},
{
"variable": "c",
"dividend": 213,
"divisor": 65,
"remainder": 18,
"description": "Let c be the remainder when f + 147 is divided by 65."
},
{
"variable": "p",
"dividend": 794,
"divisor": 96,
"remainder": 26,
"description": "Let p be the remainder when f + 728 is divided by 96."
},
{
"variable": "r",
"dividend": 639,
"divisor": 72,
"remainder": 63,
"description": "Let r be the remainder when f + 573 is divided by 72."
},
{
"variable": "q",
"dividend": 325,
"divisor": 15,
"remainder": 10,
"description": "Let q be the remainder when f + 259 is divided by 15."
},
{
"variable": "j",
"dividend": 156,
"divisor": 86,
"remainder": 70,
"description": "Let j be the remainder when f + 90 is divided by 86."
},
{
"variable": "i",
"dividend": 408,
"divisor": 36,
"remainder": 12,
"description": "Let i be the remainder when f + 342 is divided by 36."
},
{
"variable": "v",
"dividend": 882,
"divisor": 27,
"remainder": 18,
"description": "Let v be the remainder when f + 816 is divided by 27."
},
{
"variable": "x",
"dividend": 435,
"divisor": 47,
"remainder": 12,
"description": "Let x be the remainder when f + 369 is divided by 47."
},
{
"variable": "l",
"dividend": 982,
"divisor": 10,
"remainder": 2,
"description": "Let l be the remainder when c - r - v + j - p + q - i + x + 991 is divided by 10."
}
],
"final_dividend": 689,
"final_remainder": 39,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let m be the remainder when 951 is divided by 68. Let n be the remainder when 190 is divided by 56. Let y be the remainder when 349 is divided by 23. Let g be the remainder when 510 is divided by 85. Let x be the remainder when 505 is divided by 20. Let p be the remainder when x + g - m - y + n + 385 is divided by 53. Let v be the remainder when g + x - m - n - y + 885 is divided by 28. Let r be the remainder when p - v + 159 is divided by 90. Let f be the remainder when v - p + 470 is divided by 66. Let i be the remainder when f - r + 173 is divided by 49. What is the remainder when i + 940 is divided by 57?
Please reason step by step, and put your final answer within \boxed{}.
|
39
| 25
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2, 3, 4, 5 -> 6, 7 -> 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "m",
"dividend": 951,
"divisor": 68,
"remainder": 67,
"description": "Let m be the remainder when 951 is divided by 68."
},
{
"variable": "n",
"dividend": 190,
"divisor": 56,
"remainder": 22,
"description": "Let n be the remainder when 190 is divided by 56."
},
{
"variable": "y",
"dividend": 349,
"divisor": 23,
"remainder": 4,
"description": "Let y be the remainder when 349 is divided by 23."
},
{
"variable": "g",
"dividend": 510,
"divisor": 85,
"remainder": 0,
"description": "Let g be the remainder when 510 is divided by 85."
},
{
"variable": "x",
"dividend": 505,
"divisor": 20,
"remainder": 5,
"description": "Let x be the remainder when 505 is divided by 20."
},
{
"variable": "p",
"dividend": 341,
"divisor": 53,
"remainder": 23,
"description": "Let p be the remainder when x + g - m - y + n + 385 is divided by 53."
},
{
"variable": "v",
"dividend": 797,
"divisor": 28,
"remainder": 13,
"description": "Let v be the remainder when g + x - m - n - y + 885 is divided by 28."
},
{
"variable": "r",
"dividend": 169,
"divisor": 90,
"remainder": 79,
"description": "Let r be the remainder when p - v + 159 is divided by 90."
},
{
"variable": "f",
"dividend": 460,
"divisor": 66,
"remainder": 64,
"description": "Let f be the remainder when v - p + 470 is divided by 66."
},
{
"variable": "i",
"dividend": 158,
"divisor": 49,
"remainder": 11,
"description": "Let i be the remainder when f - r + 173 is divided by 49."
}
],
"final_dividend": 951,
"final_remainder": 39,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let m be the remainder when 613 is divided by 70. Let v be the remainder when 561 is divided by 17. Let h be the remainder when m - v + 771 is divided by 53. Let w be the remainder when h + 607 is divided by 66. Let r be the remainder when h + 233 is divided by 88. Let y be the remainder when h + 360 is divided by 57. Let z be the remainder when w - y - r + 287 is divided by 62. Let s be the remainder when y - w - r + 264 is divided by 96. Let q be the remainder when s - z + 632 is divided by 54. Let i be the remainder when s - z + 709 is divided by 49. What is the remainder when i - q + 476 is divided by 99?
Please reason step by step, and put your final answer within \boxed{}.
|
75
| 26
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2 -> 3 -> 4, 5, 6 -> 7, 8 -> 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "m",
"dividend": 613,
"divisor": 70,
"remainder": 53,
"description": "Let m be the remainder when 613 is divided by 70."
},
{
"variable": "v",
"dividend": 561,
"divisor": 17,
"remainder": 0,
"description": "Let v be the remainder when 561 is divided by 17."
},
{
"variable": "h",
"dividend": 824,
"divisor": 53,
"remainder": 29,
"description": "Let h be the remainder when m - v + 771 is divided by 53."
},
{
"variable": "w",
"dividend": 636,
"divisor": 66,
"remainder": 42,
"description": "Let w be the remainder when h + 607 is divided by 66."
},
{
"variable": "r",
"dividend": 262,
"divisor": 88,
"remainder": 86,
"description": "Let r be the remainder when h + 233 is divided by 88."
},
{
"variable": "y",
"dividend": 389,
"divisor": 57,
"remainder": 47,
"description": "Let y be the remainder when h + 360 is divided by 57."
},
{
"variable": "z",
"dividend": 196,
"divisor": 62,
"remainder": 10,
"description": "Let z be the remainder when w - y - r + 287 is divided by 62."
},
{
"variable": "s",
"dividend": 183,
"divisor": 96,
"remainder": 87,
"description": "Let s be the remainder when y - w - r + 264 is divided by 96."
},
{
"variable": "q",
"dividend": 709,
"divisor": 54,
"remainder": 7,
"description": "Let q be the remainder when s - z + 632 is divided by 54."
},
{
"variable": "i",
"dividend": 786,
"divisor": 49,
"remainder": 2,
"description": "Let i be the remainder when s - z + 709 is divided by 49."
}
],
"final_dividend": 471,
"final_remainder": 75,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let l be the remainder when 964 is divided by 47. Let v be the remainder when 889 is divided by 74. Let m be the remainder when l - v + 688 is divided by 77. Let g be the remainder when m + 248 is divided by 29. Let b be the remainder when m + 871 is divided by 98. Let f be the remainder when m + 820 is divided by 31. Let d be the remainder when g - f - b + 873 is divided by 15. Let t be the remainder when d + 646 is divided by 39. Let j be the remainder when t + 906 is divided by 49. Let s be the remainder when j + 430 is divided by 34. What is the remainder when s + 684 is divided by 96?
Please reason step by step, and put your final answer within \boxed{}.
|
12
| 27
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2 -> 3 -> 4, 5, 6 -> 7 -> 8 -> 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "l",
"dividend": 964,
"divisor": 47,
"remainder": 24,
"description": "Let l be the remainder when 964 is divided by 47."
},
{
"variable": "v",
"dividend": 889,
"divisor": 74,
"remainder": 1,
"description": "Let v be the remainder when 889 is divided by 74."
},
{
"variable": "m",
"dividend": 711,
"divisor": 77,
"remainder": 18,
"description": "Let m be the remainder when l - v + 688 is divided by 77."
},
{
"variable": "g",
"dividend": 266,
"divisor": 29,
"remainder": 5,
"description": "Let g be the remainder when m + 248 is divided by 29."
},
{
"variable": "b",
"dividend": 889,
"divisor": 98,
"remainder": 7,
"description": "Let b be the remainder when m + 871 is divided by 98."
},
{
"variable": "f",
"dividend": 838,
"divisor": 31,
"remainder": 1,
"description": "Let f be the remainder when m + 820 is divided by 31."
},
{
"variable": "d",
"dividend": 870,
"divisor": 15,
"remainder": 0,
"description": "Let d be the remainder when g - f - b + 873 is divided by 15."
},
{
"variable": "t",
"dividend": 646,
"divisor": 39,
"remainder": 22,
"description": "Let t be the remainder when d + 646 is divided by 39."
},
{
"variable": "j",
"dividend": 928,
"divisor": 49,
"remainder": 46,
"description": "Let j be the remainder when t + 906 is divided by 49."
},
{
"variable": "s",
"dividend": 476,
"divisor": 34,
"remainder": 0,
"description": "Let s be the remainder when j + 430 is divided by 34."
}
],
"final_dividend": 684,
"final_remainder": 12,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let i be the remainder when 592 is divided by 92. Let u be the remainder when 205 is divided by 80. Let f be the remainder when 971 is divided by 76. Let v be the remainder when 185 is divided by 46. Let b be the remainder when 560 is divided by 44. Let r be the remainder when 950 is divided by 28. Let d be the remainder when b - r - i + f - v + u + 414 is divided by 21. Let j be the remainder when d + 426 is divided by 13. Let l be the remainder when j + 433 is divided by 93. Let g be the remainder when j + 129 is divided by 27. What is the remainder when l - g + 492 is divided by 46?
Please reason step by step, and put your final answer within \boxed{}.
|
7
| 28
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2, 3, 4, 5, 6 -> 7 -> 8 -> 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "i",
"dividend": 592,
"divisor": 92,
"remainder": 40,
"description": "Let i be the remainder when 592 is divided by 92."
},
{
"variable": "u",
"dividend": 205,
"divisor": 80,
"remainder": 45,
"description": "Let u be the remainder when 205 is divided by 80."
},
{
"variable": "f",
"dividend": 971,
"divisor": 76,
"remainder": 59,
"description": "Let f be the remainder when 971 is divided by 76."
},
{
"variable": "v",
"dividend": 185,
"divisor": 46,
"remainder": 1,
"description": "Let v be the remainder when 185 is divided by 46."
},
{
"variable": "b",
"dividend": 560,
"divisor": 44,
"remainder": 32,
"description": "Let b be the remainder when 560 is divided by 44."
},
{
"variable": "r",
"dividend": 950,
"divisor": 28,
"remainder": 26,
"description": "Let r be the remainder when 950 is divided by 28."
},
{
"variable": "d",
"dividend": 483,
"divisor": 21,
"remainder": 0,
"description": "Let d be the remainder when b - r - i + f - v + u + 414 is divided by 21."
},
{
"variable": "j",
"dividend": 426,
"divisor": 13,
"remainder": 10,
"description": "Let j be the remainder when d + 426 is divided by 13."
},
{
"variable": "l",
"dividend": 443,
"divisor": 93,
"remainder": 71,
"description": "Let l be the remainder when j + 433 is divided by 93."
},
{
"variable": "g",
"dividend": 139,
"divisor": 27,
"remainder": 4,
"description": "Let g be the remainder when j + 129 is divided by 27."
}
],
"final_dividend": 559,
"final_remainder": 7,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let b be the remainder when 224 is divided by 48. Let i be the remainder when b + 497 is divided by 40. Let z be the remainder when i + 559 is divided by 89. Let h be the remainder when z + 922 is divided by 24. Let x be the remainder when z + 614 is divided by 86. Let d be the remainder when x - h + 513 is divided by 90. Let l be the remainder when d + 372 is divided by 88. Let v be the remainder when d + 437 is divided by 83. Let g be the remainder when l - v + 645 is divided by 95. Let p be the remainder when l - v + 489 is divided by 59. What is the remainder when g - p + 395 is divided by 42?
Please reason step by step, and put your final answer within \boxed{}.
|
33
| 29
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3 -> 4, 5 -> 6 -> 7, 8 -> 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "b",
"dividend": 224,
"divisor": 48,
"remainder": 32,
"description": "Let b be the remainder when 224 is divided by 48."
},
{
"variable": "i",
"dividend": 529,
"divisor": 40,
"remainder": 9,
"description": "Let i be the remainder when b + 497 is divided by 40."
},
{
"variable": "z",
"dividend": 568,
"divisor": 89,
"remainder": 34,
"description": "Let z be the remainder when i + 559 is divided by 89."
},
{
"variable": "h",
"dividend": 956,
"divisor": 24,
"remainder": 20,
"description": "Let h be the remainder when z + 922 is divided by 24."
},
{
"variable": "x",
"dividend": 648,
"divisor": 86,
"remainder": 46,
"description": "Let x be the remainder when z + 614 is divided by 86."
},
{
"variable": "d",
"dividend": 539,
"divisor": 90,
"remainder": 89,
"description": "Let d be the remainder when x - h + 513 is divided by 90."
},
{
"variable": "l",
"dividend": 461,
"divisor": 88,
"remainder": 21,
"description": "Let l be the remainder when d + 372 is divided by 88."
},
{
"variable": "v",
"dividend": 526,
"divisor": 83,
"remainder": 28,
"description": "Let v be the remainder when d + 437 is divided by 83."
},
{
"variable": "g",
"dividend": 638,
"divisor": 95,
"remainder": 68,
"description": "Let g be the remainder when l - v + 645 is divided by 95."
},
{
"variable": "p",
"dividend": 482,
"divisor": 59,
"remainder": 10,
"description": "Let p be the remainder when l - v + 489 is divided by 59."
}
],
"final_dividend": 453,
"final_remainder": 33,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let z be the remainder when 746 is divided by 71. Let t be the remainder when z + 128 is divided by 27. Let f be the remainder when t + 135 is divided by 68. Let q be the remainder when t + 142 is divided by 35. Let b be the remainder when q - f + 356 is divided by 15. Let i be the remainder when b + 281 is divided by 92. Let a be the remainder when b + 968 is divided by 55. Let p be the remainder when b + 425 is divided by 93. Let v be the remainder when p - i - a + 290 is divided by 25. Let s be the remainder when p - i - a + 179 is divided by 98. What is the remainder when s - v + 115 is divided by 65?
Please reason step by step, and put your final answer within \boxed{}.
|
51
| 30
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3, 4 -> 5 -> 6, 7, 8 -> 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "z",
"dividend": 746,
"divisor": 71,
"remainder": 36,
"description": "Let z be the remainder when 746 is divided by 71."
},
{
"variable": "t",
"dividend": 164,
"divisor": 27,
"remainder": 2,
"description": "Let t be the remainder when z + 128 is divided by 27."
},
{
"variable": "f",
"dividend": 137,
"divisor": 68,
"remainder": 1,
"description": "Let f be the remainder when t + 135 is divided by 68."
},
{
"variable": "q",
"dividend": 144,
"divisor": 35,
"remainder": 4,
"description": "Let q be the remainder when t + 142 is divided by 35."
},
{
"variable": "b",
"dividend": 359,
"divisor": 15,
"remainder": 14,
"description": "Let b be the remainder when q - f + 356 is divided by 15."
},
{
"variable": "i",
"dividend": 295,
"divisor": 92,
"remainder": 19,
"description": "Let i be the remainder when b + 281 is divided by 92."
},
{
"variable": "a",
"dividend": 982,
"divisor": 55,
"remainder": 47,
"description": "Let a be the remainder when b + 968 is divided by 55."
},
{
"variable": "p",
"dividend": 439,
"divisor": 93,
"remainder": 67,
"description": "Let p be the remainder when b + 425 is divided by 93."
},
{
"variable": "v",
"dividend": 291,
"divisor": 25,
"remainder": 16,
"description": "Let v be the remainder when p - i - a + 290 is divided by 25."
},
{
"variable": "s",
"dividend": 180,
"divisor": 98,
"remainder": 82,
"description": "Let s be the remainder when p - i - a + 179 is divided by 98."
}
],
"final_dividend": 181,
"final_remainder": 51,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let i be the remainder when 729 is divided by 55. Let g be the remainder when 754 is divided by 45. Let l be the remainder when 787 is divided by 19. Let n be the remainder when 472 is divided by 61. Let m be the remainder when 263 is divided by 96. Let d be the remainder when 969 is divided by 28. Let k be the remainder when l - n - m + d - i - g + 619 is divided by 14. Let t be the remainder when n - i + d + l + g - m + 611 is divided by 19. Let o be the remainder when d - g - n + m + l + i + 942 is divided by 81. Let c be the remainder when d - m - l - i + n + g + 909 is divided by 67. What is the remainder when c + o - k + t + 428 is divided by 56?
Please reason step by step, and put your final answer within \boxed{}.
|
21
| 31
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2, 3, 4, 5, 6 -> 7, 8, 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "i",
"dividend": 729,
"divisor": 55,
"remainder": 14,
"description": "Let i be the remainder when 729 is divided by 55."
},
{
"variable": "g",
"dividend": 754,
"divisor": 45,
"remainder": 34,
"description": "Let g be the remainder when 754 is divided by 45."
},
{
"variable": "l",
"dividend": 787,
"divisor": 19,
"remainder": 8,
"description": "Let l be the remainder when 787 is divided by 19."
},
{
"variable": "n",
"dividend": 472,
"divisor": 61,
"remainder": 45,
"description": "Let n be the remainder when 472 is divided by 61."
},
{
"variable": "m",
"dividend": 263,
"divisor": 96,
"remainder": 71,
"description": "Let m be the remainder when 263 is divided by 96."
},
{
"variable": "d",
"dividend": 969,
"divisor": 28,
"remainder": 17,
"description": "Let d be the remainder when 969 is divided by 28."
},
{
"variable": "k",
"dividend": 480,
"divisor": 14,
"remainder": 4,
"description": "Let k be the remainder when l - n - m + d - i - g + 619 is divided by 14."
},
{
"variable": "t",
"dividend": 630,
"divisor": 19,
"remainder": 3,
"description": "Let t be the remainder when n - i + d + l + g - m + 611 is divided by 19."
},
{
"variable": "o",
"dividend": 973,
"divisor": 81,
"remainder": 1,
"description": "Let o be the remainder when d - g - n + m + l + i + 942 is divided by 81."
},
{
"variable": "c",
"dividend": 912,
"divisor": 67,
"remainder": 41,
"description": "Let c be the remainder when d - m - l - i + n + g + 909 is divided by 67."
}
],
"final_dividend": 469,
"final_remainder": 21,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let f be the remainder when 943 is divided by 62. Let x be the remainder when 228 is divided by 19. Let q be the remainder when 175 is divided by 92. Let j be the remainder when f - x + q + 10 is divided by 69. Let i be the remainder when j + 593 is divided by 25. Let t be the remainder when i + 263 is divided by 48. Let y be the remainder when i + 821 is divided by 51. Let v be the remainder when i + 626 is divided by 54. Let n be the remainder when i + 351 is divided by 20. Let h be the remainder when i + 659 is divided by 91. What is the remainder when h + t + n - v + y + 901 is divided by 45?
Please reason step by step, and put your final answer within \boxed{}.
|
0
| 32
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2, 3 -> 4 -> 5 -> 6, 7, 8, 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "f",
"dividend": 943,
"divisor": 62,
"remainder": 13,
"description": "Let f be the remainder when 943 is divided by 62."
},
{
"variable": "x",
"dividend": 228,
"divisor": 19,
"remainder": 0,
"description": "Let x be the remainder when 228 is divided by 19."
},
{
"variable": "q",
"dividend": 175,
"divisor": 92,
"remainder": 83,
"description": "Let q be the remainder when 175 is divided by 92."
},
{
"variable": "j",
"dividend": 106,
"divisor": 69,
"remainder": 37,
"description": "Let j be the remainder when f - x + q + 10 is divided by 69."
},
{
"variable": "i",
"dividend": 630,
"divisor": 25,
"remainder": 5,
"description": "Let i be the remainder when j + 593 is divided by 25."
},
{
"variable": "t",
"dividend": 268,
"divisor": 48,
"remainder": 28,
"description": "Let t be the remainder when i + 263 is divided by 48."
},
{
"variable": "y",
"dividend": 826,
"divisor": 51,
"remainder": 10,
"description": "Let y be the remainder when i + 821 is divided by 51."
},
{
"variable": "v",
"dividend": 631,
"divisor": 54,
"remainder": 37,
"description": "Let v be the remainder when i + 626 is divided by 54."
},
{
"variable": "n",
"dividend": 356,
"divisor": 20,
"remainder": 16,
"description": "Let n be the remainder when i + 351 is divided by 20."
},
{
"variable": "h",
"dividend": 664,
"divisor": 91,
"remainder": 27,
"description": "Let h be the remainder when i + 659 is divided by 91."
}
],
"final_dividend": 945,
"final_remainder": 0,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let r be the remainder when 594 is divided by 48. Let b be the remainder when r + 497 is divided by 97. Let q be the remainder when b + 144 is divided by 68. Let i be the remainder when q + 512 is divided by 30. Let w be the remainder when q + 537 is divided by 71. Let s be the remainder when i - w + 505 is divided by 53. Let p be the remainder when i - w + 574 is divided by 57. Let l be the remainder when p - s + 175 is divided by 44. Let x be the remainder when s - p + 667 is divided by 59. Let o be the remainder when s - p + 976 is divided by 34. What is the remainder when o - l - x + 393 is divided by 49?
Please reason step by step, and put your final answer within \boxed{}.
|
3
| 33
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3 -> 4, 5 -> 6, 7 -> 8, 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "r",
"dividend": 594,
"divisor": 48,
"remainder": 18,
"description": "Let r be the remainder when 594 is divided by 48."
},
{
"variable": "b",
"dividend": 515,
"divisor": 97,
"remainder": 30,
"description": "Let b be the remainder when r + 497 is divided by 97."
},
{
"variable": "q",
"dividend": 174,
"divisor": 68,
"remainder": 38,
"description": "Let q be the remainder when b + 144 is divided by 68."
},
{
"variable": "i",
"dividend": 550,
"divisor": 30,
"remainder": 10,
"description": "Let i be the remainder when q + 512 is divided by 30."
},
{
"variable": "w",
"dividend": 575,
"divisor": 71,
"remainder": 7,
"description": "Let w be the remainder when q + 537 is divided by 71."
},
{
"variable": "s",
"dividend": 508,
"divisor": 53,
"remainder": 31,
"description": "Let s be the remainder when i - w + 505 is divided by 53."
},
{
"variable": "p",
"dividend": 577,
"divisor": 57,
"remainder": 7,
"description": "Let p be the remainder when i - w + 574 is divided by 57."
},
{
"variable": "l",
"dividend": 151,
"divisor": 44,
"remainder": 19,
"description": "Let l be the remainder when p - s + 175 is divided by 44."
},
{
"variable": "x",
"dividend": 691,
"divisor": 59,
"remainder": 42,
"description": "Let x be the remainder when s - p + 667 is divided by 59."
},
{
"variable": "o",
"dividend": 1000,
"divisor": 34,
"remainder": 14,
"description": "Let o be the remainder when s - p + 976 is divided by 34."
}
],
"final_dividend": 346,
"final_remainder": 3,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let h be the remainder when 237 is divided by 65. Let p be the remainder when h + 840 is divided by 56. Let g be the remainder when h + 104 is divided by 56. Let j be the remainder when g - p + 503 is divided by 16. Let r be the remainder when j + 867 is divided by 67. Let z be the remainder when j + 930 is divided by 45. Let t be the remainder when j + 184 is divided by 26. Let n be the remainder when j + 898 is divided by 57. Let x be the remainder when j + 459 is divided by 81. Let c be the remainder when z + r + t - n - x + 673 is divided by 35. What is the remainder when c + 251 is divided by 68?
Please reason step by step, and put your final answer within \boxed{}.
|
48
| 34
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2, 3 -> 4 -> 5, 6, 7, 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "h",
"dividend": 237,
"divisor": 65,
"remainder": 42,
"description": "Let h be the remainder when 237 is divided by 65."
},
{
"variable": "p",
"dividend": 882,
"divisor": 56,
"remainder": 42,
"description": "Let p be the remainder when h + 840 is divided by 56."
},
{
"variable": "g",
"dividend": 146,
"divisor": 56,
"remainder": 34,
"description": "Let g be the remainder when h + 104 is divided by 56."
},
{
"variable": "j",
"dividend": 495,
"divisor": 16,
"remainder": 15,
"description": "Let j be the remainder when g - p + 503 is divided by 16."
},
{
"variable": "r",
"dividend": 882,
"divisor": 67,
"remainder": 11,
"description": "Let r be the remainder when j + 867 is divided by 67."
},
{
"variable": "z",
"dividend": 945,
"divisor": 45,
"remainder": 0,
"description": "Let z be the remainder when j + 930 is divided by 45."
},
{
"variable": "t",
"dividend": 199,
"divisor": 26,
"remainder": 17,
"description": "Let t be the remainder when j + 184 is divided by 26."
},
{
"variable": "n",
"dividend": 913,
"divisor": 57,
"remainder": 1,
"description": "Let n be the remainder when j + 898 is divided by 57."
},
{
"variable": "x",
"dividend": 474,
"divisor": 81,
"remainder": 69,
"description": "Let x be the remainder when j + 459 is divided by 81."
},
{
"variable": "c",
"dividend": 631,
"divisor": 35,
"remainder": 1,
"description": "Let c be the remainder when z + r + t - n - x + 673 is divided by 35."
}
],
"final_dividend": 252,
"final_remainder": 48,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let j be the remainder when 477 is divided by 12. Let q be the remainder when j + 203 is divided by 96. Let g be the remainder when j + 406 is divided by 84. Let n be the remainder when j + 702 is divided by 13. Let x be the remainder when g - q + n + 568 is divided by 43. Let f be the remainder when n - g + q + 601 is divided by 58. Let a be the remainder when n - g - q + 1083 is divided by 63. Let p be the remainder when n - g - q + 367 is divided by 100. Let k be the remainder when g - n - q + 302 is divided by 78. Let w be the remainder when g - q - n + 756 is divided by 81. What is the remainder when k - x - f - w - a + p + 468 is divided by 100?
Please reason step by step, and put your final answer within \boxed{}.
|
97
| 35
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2, 3, 4 -> 5, 6, 7, 8, 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "j",
"dividend": 477,
"divisor": 12,
"remainder": 9,
"description": "Let j be the remainder when 477 is divided by 12."
},
{
"variable": "q",
"dividend": 212,
"divisor": 96,
"remainder": 20,
"description": "Let q be the remainder when j + 203 is divided by 96."
},
{
"variable": "g",
"dividend": 415,
"divisor": 84,
"remainder": 79,
"description": "Let g be the remainder when j + 406 is divided by 84."
},
{
"variable": "n",
"dividend": 711,
"divisor": 13,
"remainder": 9,
"description": "Let n be the remainder when j + 702 is divided by 13."
},
{
"variable": "x",
"dividend": 636,
"divisor": 43,
"remainder": 34,
"description": "Let x be the remainder when g - q + n + 568 is divided by 43."
},
{
"variable": "f",
"dividend": 551,
"divisor": 58,
"remainder": 29,
"description": "Let f be the remainder when n - g + q + 601 is divided by 58."
},
{
"variable": "a",
"dividend": 993,
"divisor": 63,
"remainder": 48,
"description": "Let a be the remainder when n - g - q + 1083 is divided by 63."
},
{
"variable": "p",
"dividend": 277,
"divisor": 100,
"remainder": 77,
"description": "Let p be the remainder when n - g - q + 367 is divided by 100."
},
{
"variable": "k",
"dividend": 352,
"divisor": 78,
"remainder": 40,
"description": "Let k be the remainder when g - n - q + 302 is divided by 78."
},
{
"variable": "w",
"dividend": 806,
"divisor": 81,
"remainder": 77,
"description": "Let w be the remainder when g - q - n + 756 is divided by 81."
}
],
"final_dividend": 397,
"final_remainder": 97,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let a be the remainder when 675 is divided by 44. Let n be the remainder when a + 225 is divided by 44. Let h be the remainder when a + 843 is divided by 88. Let r be the remainder when n - h + 199 is divided by 40. Let v be the remainder when h - n + 751 is divided by 62. Let k be the remainder when n - h + 812 is divided by 10. Let c be the remainder when h - n + 841 is divided by 46. Let i be the remainder when h - n + 911 is divided by 93. Let y be the remainder when k + v - r + i - c + 351 is divided by 14. Let f be the remainder when y + 643 is divided by 92. What is the remainder when f + 593 is divided by 77?
Please reason step by step, and put your final answer within \boxed{}.
|
66
| 36
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2, 3 -> 4, 5, 6, 7, 8 -> 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "a",
"dividend": 675,
"divisor": 44,
"remainder": 15,
"description": "Let a be the remainder when 675 is divided by 44."
},
{
"variable": "n",
"dividend": 240,
"divisor": 44,
"remainder": 20,
"description": "Let n be the remainder when a + 225 is divided by 44."
},
{
"variable": "h",
"dividend": 858,
"divisor": 88,
"remainder": 66,
"description": "Let h be the remainder when a + 843 is divided by 88."
},
{
"variable": "r",
"dividend": 153,
"divisor": 40,
"remainder": 33,
"description": "Let r be the remainder when n - h + 199 is divided by 40."
},
{
"variable": "v",
"dividend": 797,
"divisor": 62,
"remainder": 53,
"description": "Let v be the remainder when h - n + 751 is divided by 62."
},
{
"variable": "k",
"dividend": 766,
"divisor": 10,
"remainder": 6,
"description": "Let k be the remainder when n - h + 812 is divided by 10."
},
{
"variable": "c",
"dividend": 887,
"divisor": 46,
"remainder": 13,
"description": "Let c be the remainder when h - n + 841 is divided by 46."
},
{
"variable": "i",
"dividend": 957,
"divisor": 93,
"remainder": 27,
"description": "Let i be the remainder when h - n + 911 is divided by 93."
},
{
"variable": "y",
"dividend": 391,
"divisor": 14,
"remainder": 13,
"description": "Let y be the remainder when k + v - r + i - c + 351 is divided by 14."
},
{
"variable": "f",
"dividend": 656,
"divisor": 92,
"remainder": 12,
"description": "Let f be the remainder when y + 643 is divided by 92."
}
],
"final_dividend": 605,
"final_remainder": 66,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let z be the remainder when 114 is divided by 33. Let f be the remainder when z + 894 is divided by 53. Let p be the remainder when z + 775 is divided by 82. Let k be the remainder when z + 710 is divided by 32. Let n be the remainder when f - k + p + 250 is divided by 61. Let v be the remainder when n + 386 is divided by 71. Let c be the remainder when n + 322 is divided by 10. Let m be the remainder when c - v + 694 is divided by 40. Let d be the remainder when c - v + 574 is divided by 43. Let a be the remainder when c - v + 752 is divided by 30. What is the remainder when a + m - d + 253 is divided by 47?
Please reason step by step, and put your final answer within \boxed{}.
|
21
| 37
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2, 3, 4 -> 5 -> 6, 7 -> 8, 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "z",
"dividend": 114,
"divisor": 33,
"remainder": 15,
"description": "Let z be the remainder when 114 is divided by 33."
},
{
"variable": "f",
"dividend": 909,
"divisor": 53,
"remainder": 8,
"description": "Let f be the remainder when z + 894 is divided by 53."
},
{
"variable": "p",
"dividend": 790,
"divisor": 82,
"remainder": 52,
"description": "Let p be the remainder when z + 775 is divided by 82."
},
{
"variable": "k",
"dividend": 725,
"divisor": 32,
"remainder": 21,
"description": "Let k be the remainder when z + 710 is divided by 32."
},
{
"variable": "n",
"dividend": 289,
"divisor": 61,
"remainder": 45,
"description": "Let n be the remainder when f - k + p + 250 is divided by 61."
},
{
"variable": "v",
"dividend": 431,
"divisor": 71,
"remainder": 5,
"description": "Let v be the remainder when n + 386 is divided by 71."
},
{
"variable": "c",
"dividend": 367,
"divisor": 10,
"remainder": 7,
"description": "Let c be the remainder when n + 322 is divided by 10."
},
{
"variable": "m",
"dividend": 696,
"divisor": 40,
"remainder": 16,
"description": "Let m be the remainder when c - v + 694 is divided by 40."
},
{
"variable": "d",
"dividend": 576,
"divisor": 43,
"remainder": 17,
"description": "Let d be the remainder when c - v + 574 is divided by 43."
},
{
"variable": "a",
"dividend": 754,
"divisor": 30,
"remainder": 4,
"description": "Let a be the remainder when c - v + 752 is divided by 30."
}
],
"final_dividend": 256,
"final_remainder": 21,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let l be the remainder when 214 is divided by 82. Let i be the remainder when 617 is divided by 80. Let s be the remainder when 649 is divided by 83. Let k be the remainder when 435 is divided by 31. Let r be the remainder when 219 is divided by 66. Let q be the remainder when r - i + s - l - k + 696 is divided by 84. Let v be the remainder when q + 568 is divided by 81. Let a be the remainder when v + 499 is divided by 12. Let w be the remainder when v + 857 is divided by 10. Let h be the remainder when v + 168 is divided by 84. What is the remainder when a - h + w + 134 is divided by 15?
Please reason step by step, and put your final answer within \boxed{}.
|
12
| 38
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2, 3, 4, 5 -> 6 -> 7 -> 8, 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "l",
"dividend": 214,
"divisor": 82,
"remainder": 50,
"description": "Let l be the remainder when 214 is divided by 82."
},
{
"variable": "i",
"dividend": 617,
"divisor": 80,
"remainder": 57,
"description": "Let i be the remainder when 617 is divided by 80."
},
{
"variable": "s",
"dividend": 649,
"divisor": 83,
"remainder": 68,
"description": "Let s be the remainder when 649 is divided by 83."
},
{
"variable": "k",
"dividend": 435,
"divisor": 31,
"remainder": 1,
"description": "Let k be the remainder when 435 is divided by 31."
},
{
"variable": "r",
"dividend": 219,
"divisor": 66,
"remainder": 21,
"description": "Let r be the remainder when 219 is divided by 66."
},
{
"variable": "q",
"dividend": 677,
"divisor": 84,
"remainder": 5,
"description": "Let q be the remainder when r - i + s - l - k + 696 is divided by 84."
},
{
"variable": "v",
"dividend": 573,
"divisor": 81,
"remainder": 6,
"description": "Let v be the remainder when q + 568 is divided by 81."
},
{
"variable": "a",
"dividend": 505,
"divisor": 12,
"remainder": 1,
"description": "Let a be the remainder when v + 499 is divided by 12."
},
{
"variable": "w",
"dividend": 863,
"divisor": 10,
"remainder": 3,
"description": "Let w be the remainder when v + 857 is divided by 10."
},
{
"variable": "h",
"dividend": 174,
"divisor": 84,
"remainder": 6,
"description": "Let h be the remainder when v + 168 is divided by 84."
}
],
"final_dividend": 132,
"final_remainder": 12,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let u be the remainder when 799 is divided by 20. Let z be the remainder when 236 is divided by 79. Let o be the remainder when 221 is divided by 54. Let t be the remainder when o - u + z + 510 is divided by 78. Let m be the remainder when t + 616 is divided by 64. Let g be the remainder when t + 325 is divided by 39. Let b be the remainder when t + 230 is divided by 54. Let j be the remainder when t + 968 is divided by 34. Let l be the remainder when t + 900 is divided by 14. Let n be the remainder when t + 856 is divided by 88. What is the remainder when b - l + j + m - n - g + 293 is divided by 12?
Please reason step by step, and put your final answer within \boxed{}.
|
3
| 39
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2, 3 -> 4 -> 5, 6, 7, 8, 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "u",
"dividend": 799,
"divisor": 20,
"remainder": 19,
"description": "Let u be the remainder when 799 is divided by 20."
},
{
"variable": "z",
"dividend": 236,
"divisor": 79,
"remainder": 78,
"description": "Let z be the remainder when 236 is divided by 79."
},
{
"variable": "o",
"dividend": 221,
"divisor": 54,
"remainder": 5,
"description": "Let o be the remainder when 221 is divided by 54."
},
{
"variable": "t",
"dividend": 574,
"divisor": 78,
"remainder": 28,
"description": "Let t be the remainder when o - u + z + 510 is divided by 78."
},
{
"variable": "m",
"dividend": 644,
"divisor": 64,
"remainder": 4,
"description": "Let m be the remainder when t + 616 is divided by 64."
},
{
"variable": "g",
"dividend": 353,
"divisor": 39,
"remainder": 2,
"description": "Let g be the remainder when t + 325 is divided by 39."
},
{
"variable": "b",
"dividend": 258,
"divisor": 54,
"remainder": 42,
"description": "Let b be the remainder when t + 230 is divided by 54."
},
{
"variable": "j",
"dividend": 996,
"divisor": 34,
"remainder": 10,
"description": "Let j be the remainder when t + 968 is divided by 34."
},
{
"variable": "l",
"dividend": 928,
"divisor": 14,
"remainder": 4,
"description": "Let l be the remainder when t + 900 is divided by 14."
},
{
"variable": "n",
"dividend": 884,
"divisor": 88,
"remainder": 4,
"description": "Let n be the remainder when t + 856 is divided by 88."
}
],
"final_dividend": 339,
"final_remainder": 3,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let v be the remainder when 633 is divided by 94. Let s be the remainder when v + 338 is divided by 62. Let q be the remainder when s + 635 is divided by 17. Let o be the remainder when q + 734 is divided by 32. Let w be the remainder when q + 600 is divided by 81. Let i be the remainder when w - o + 217 is divided by 54. Let x be the remainder when o - w + 1004 is divided by 58. Let h be the remainder when o - w + 710 is divided by 48. Let t be the remainder when i - x - h + 316 is divided by 63. Let m be the remainder when x - h + i + 78 is divided by 92. What is the remainder when m - t + 919 is divided by 44?
Please reason step by step, and put your final answer within \boxed{}.
|
43
| 40
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3 -> 4, 5 -> 6, 7, 8 -> 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "v",
"dividend": 633,
"divisor": 94,
"remainder": 69,
"description": "Let v be the remainder when 633 is divided by 94."
},
{
"variable": "s",
"dividend": 407,
"divisor": 62,
"remainder": 35,
"description": "Let s be the remainder when v + 338 is divided by 62."
},
{
"variable": "q",
"dividend": 670,
"divisor": 17,
"remainder": 7,
"description": "Let q be the remainder when s + 635 is divided by 17."
},
{
"variable": "o",
"dividend": 741,
"divisor": 32,
"remainder": 5,
"description": "Let o be the remainder when q + 734 is divided by 32."
},
{
"variable": "w",
"dividend": 607,
"divisor": 81,
"remainder": 40,
"description": "Let w be the remainder when q + 600 is divided by 81."
},
{
"variable": "i",
"dividend": 252,
"divisor": 54,
"remainder": 36,
"description": "Let i be the remainder when w - o + 217 is divided by 54."
},
{
"variable": "x",
"dividend": 969,
"divisor": 58,
"remainder": 41,
"description": "Let x be the remainder when o - w + 1004 is divided by 58."
},
{
"variable": "h",
"dividend": 675,
"divisor": 48,
"remainder": 3,
"description": "Let h be the remainder when o - w + 710 is divided by 48."
},
{
"variable": "t",
"dividend": 308,
"divisor": 63,
"remainder": 56,
"description": "Let t be the remainder when i - x - h + 316 is divided by 63."
},
{
"variable": "m",
"dividend": 152,
"divisor": 92,
"remainder": 60,
"description": "Let m be the remainder when x - h + i + 78 is divided by 92."
}
],
"final_dividend": 923,
"final_remainder": 43,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let n be the remainder when 348 is divided by 71. Let z be the remainder when n + 756 is divided by 87. Let k be the remainder when n + 281 is divided by 60. Let x be the remainder when k - z + 407 is divided by 51. Let p be the remainder when k - z + 914 is divided by 56. Let a be the remainder when z - k + 154 is divided by 50. Let f be the remainder when p - x - a + 429 is divided by 38. Let c be the remainder when f + 415 is divided by 35. Let h be the remainder when c + 666 is divided by 58. Let j be the remainder when h + 618 is divided by 73. What is the remainder when j + 795 is divided by 93?
Please reason step by step, and put your final answer within \boxed{}.
|
57
| 41
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2, 3 -> 4, 5, 6 -> 7 -> 8 -> 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "n",
"dividend": 348,
"divisor": 71,
"remainder": 64,
"description": "Let n be the remainder when 348 is divided by 71."
},
{
"variable": "z",
"dividend": 820,
"divisor": 87,
"remainder": 37,
"description": "Let z be the remainder when n + 756 is divided by 87."
},
{
"variable": "k",
"dividend": 345,
"divisor": 60,
"remainder": 45,
"description": "Let k be the remainder when n + 281 is divided by 60."
},
{
"variable": "x",
"dividend": 415,
"divisor": 51,
"remainder": 7,
"description": "Let x be the remainder when k - z + 407 is divided by 51."
},
{
"variable": "p",
"dividend": 922,
"divisor": 56,
"remainder": 26,
"description": "Let p be the remainder when k - z + 914 is divided by 56."
},
{
"variable": "a",
"dividend": 146,
"divisor": 50,
"remainder": 46,
"description": "Let a be the remainder when z - k + 154 is divided by 50."
},
{
"variable": "f",
"dividend": 402,
"divisor": 38,
"remainder": 22,
"description": "Let f be the remainder when p - x - a + 429 is divided by 38."
},
{
"variable": "c",
"dividend": 437,
"divisor": 35,
"remainder": 17,
"description": "Let c be the remainder when f + 415 is divided by 35."
},
{
"variable": "h",
"dividend": 683,
"divisor": 58,
"remainder": 45,
"description": "Let h be the remainder when c + 666 is divided by 58."
},
{
"variable": "j",
"dividend": 663,
"divisor": 73,
"remainder": 6,
"description": "Let j be the remainder when h + 618 is divided by 73."
}
],
"final_dividend": 801,
"final_remainder": 57,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let n be the remainder when 600 is divided by 79. Let t be the remainder when 757 is divided by 79. Let i be the remainder when 134 is divided by 77. Let h be the remainder when 149 is divided by 95. Let d be the remainder when 240 is divided by 62. Let c be the remainder when 824 is divided by 18. Let q be the remainder when c - n - i + h - d + t + 161 is divided by 11. Let f be the remainder when h + t + c + n - i + d + 1 is divided by 45. Let a be the remainder when q - f + 695 is divided by 60. Let w be the remainder when a + 313 is divided by 99. What is the remainder when w + 766 is divided by 48?
Please reason step by step, and put your final answer within \boxed{}.
|
32
| 42
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2, 3, 4, 5, 6 -> 7, 8 -> 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "n",
"dividend": 600,
"divisor": 79,
"remainder": 47,
"description": "Let n be the remainder when 600 is divided by 79."
},
{
"variable": "t",
"dividend": 757,
"divisor": 79,
"remainder": 46,
"description": "Let t be the remainder when 757 is divided by 79."
},
{
"variable": "i",
"dividend": 134,
"divisor": 77,
"remainder": 57,
"description": "Let i be the remainder when 134 is divided by 77."
},
{
"variable": "h",
"dividend": 149,
"divisor": 95,
"remainder": 54,
"description": "Let h be the remainder when 149 is divided by 95."
},
{
"variable": "d",
"dividend": 240,
"divisor": 62,
"remainder": 54,
"description": "Let d be the remainder when 240 is divided by 62."
},
{
"variable": "c",
"dividend": 824,
"divisor": 18,
"remainder": 14,
"description": "Let c be the remainder when 824 is divided by 18."
},
{
"variable": "q",
"dividend": 117,
"divisor": 11,
"remainder": 7,
"description": "Let q be the remainder when c - n - i + h - d + t + 161 is divided by 11."
},
{
"variable": "f",
"dividend": 159,
"divisor": 45,
"remainder": 24,
"description": "Let f be the remainder when h + t + c + n - i + d + 1 is divided by 45."
},
{
"variable": "a",
"dividend": 678,
"divisor": 60,
"remainder": 18,
"description": "Let a be the remainder when q - f + 695 is divided by 60."
},
{
"variable": "w",
"dividend": 331,
"divisor": 99,
"remainder": 34,
"description": "Let w be the remainder when a + 313 is divided by 99."
}
],
"final_dividend": 800,
"final_remainder": 32,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let z be the remainder when 184 is divided by 31. Let j be the remainder when z + 731 is divided by 65. Let q be the remainder when j + 933 is divided by 82. Let h be the remainder when q + 67 is divided by 77. Let s be the remainder when q + 912 is divided by 37. Let n be the remainder when q + 301 is divided by 70. Let l be the remainder when q + 724 is divided by 19. Let w be the remainder when q + 601 is divided by 79. Let p be the remainder when w - s - l + h + n + 2 is divided by 32. Let r be the remainder when p + 857 is divided by 59. What is the remainder when r + 862 is divided by 27?
Please reason step by step, and put your final answer within \boxed{}.
|
18
| 43
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3 -> 4, 5, 6, 7, 8 -> 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "z",
"dividend": 184,
"divisor": 31,
"remainder": 29,
"description": "Let z be the remainder when 184 is divided by 31."
},
{
"variable": "j",
"dividend": 760,
"divisor": 65,
"remainder": 45,
"description": "Let j be the remainder when z + 731 is divided by 65."
},
{
"variable": "q",
"dividend": 978,
"divisor": 82,
"remainder": 76,
"description": "Let q be the remainder when j + 933 is divided by 82."
},
{
"variable": "h",
"dividend": 143,
"divisor": 77,
"remainder": 66,
"description": "Let h be the remainder when q + 67 is divided by 77."
},
{
"variable": "s",
"dividend": 988,
"divisor": 37,
"remainder": 26,
"description": "Let s be the remainder when q + 912 is divided by 37."
},
{
"variable": "n",
"dividend": 377,
"divisor": 70,
"remainder": 27,
"description": "Let n be the remainder when q + 301 is divided by 70."
},
{
"variable": "l",
"dividend": 800,
"divisor": 19,
"remainder": 2,
"description": "Let l be the remainder when q + 724 is divided by 19."
},
{
"variable": "w",
"dividend": 677,
"divisor": 79,
"remainder": 45,
"description": "Let w be the remainder when q + 601 is divided by 79."
},
{
"variable": "p",
"dividend": 112,
"divisor": 32,
"remainder": 16,
"description": "Let p be the remainder when w - s - l + h + n + 2 is divided by 32."
},
{
"variable": "r",
"dividend": 873,
"divisor": 59,
"remainder": 47,
"description": "Let r be the remainder when p + 857 is divided by 59."
}
],
"final_dividend": 909,
"final_remainder": 18,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let f be the remainder when 130 is divided by 51. Let r be the remainder when f + 874 is divided by 44. Let g be the remainder when f + 305 is divided by 72. Let c be the remainder when g - r + 773 is divided by 80. Let o be the remainder when c + 413 is divided by 94. Let l be the remainder when c + 326 is divided by 89. Let y be the remainder when o - l + 516 is divided by 19. Let u be the remainder when y + 410 is divided by 59. Let n be the remainder when y + 179 is divided by 23. Let d be the remainder when y + 541 is divided by 49. What is the remainder when d - u + n + 545 is divided by 56?
Please reason step by step, and put your final answer within \boxed{}.
|
55
| 44
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2, 3 -> 4 -> 5, 6 -> 7 -> 8, 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "f",
"dividend": 130,
"divisor": 51,
"remainder": 28,
"description": "Let f be the remainder when 130 is divided by 51."
},
{
"variable": "r",
"dividend": 902,
"divisor": 44,
"remainder": 22,
"description": "Let r be the remainder when f + 874 is divided by 44."
},
{
"variable": "g",
"dividend": 333,
"divisor": 72,
"remainder": 45,
"description": "Let g be the remainder when f + 305 is divided by 72."
},
{
"variable": "c",
"dividend": 796,
"divisor": 80,
"remainder": 76,
"description": "Let c be the remainder when g - r + 773 is divided by 80."
},
{
"variable": "o",
"dividend": 489,
"divisor": 94,
"remainder": 19,
"description": "Let o be the remainder when c + 413 is divided by 94."
},
{
"variable": "l",
"dividend": 402,
"divisor": 89,
"remainder": 46,
"description": "Let l be the remainder when c + 326 is divided by 89."
},
{
"variable": "y",
"dividend": 489,
"divisor": 19,
"remainder": 14,
"description": "Let y be the remainder when o - l + 516 is divided by 19."
},
{
"variable": "u",
"dividend": 424,
"divisor": 59,
"remainder": 11,
"description": "Let u be the remainder when y + 410 is divided by 59."
},
{
"variable": "n",
"dividend": 193,
"divisor": 23,
"remainder": 9,
"description": "Let n be the remainder when y + 179 is divided by 23."
},
{
"variable": "d",
"dividend": 555,
"divisor": 49,
"remainder": 16,
"description": "Let d be the remainder when y + 541 is divided by 49."
}
],
"final_dividend": 559,
"final_remainder": 55,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let p be the remainder when 497 is divided by 62. Let l be the remainder when 348 is divided by 81. Let r be the remainder when p - l + 265 is divided by 76. Let q be the remainder when r + 360 is divided by 48. Let x be the remainder when q + 126 is divided by 28. Let k be the remainder when q + 344 is divided by 65. Let b be the remainder when x - k + 390 is divided by 48. Let j be the remainder when x - k + 242 is divided by 90. Let u be the remainder when x - k + 956 is divided by 48. Let o be the remainder when b - u - j + 736 is divided by 66. What is the remainder when o + 248 is divided by 98?
Please reason step by step, and put your final answer within \boxed{}.
|
11
| 45
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2 -> 3 -> 4 -> 5, 6 -> 7, 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "p",
"dividend": 497,
"divisor": 62,
"remainder": 1,
"description": "Let p be the remainder when 497 is divided by 62."
},
{
"variable": "l",
"dividend": 348,
"divisor": 81,
"remainder": 24,
"description": "Let l be the remainder when 348 is divided by 81."
},
{
"variable": "r",
"dividend": 242,
"divisor": 76,
"remainder": 14,
"description": "Let r be the remainder when p - l + 265 is divided by 76."
},
{
"variable": "q",
"dividend": 374,
"divisor": 48,
"remainder": 38,
"description": "Let q be the remainder when r + 360 is divided by 48."
},
{
"variable": "x",
"dividend": 164,
"divisor": 28,
"remainder": 24,
"description": "Let x be the remainder when q + 126 is divided by 28."
},
{
"variable": "k",
"dividend": 382,
"divisor": 65,
"remainder": 57,
"description": "Let k be the remainder when q + 344 is divided by 65."
},
{
"variable": "b",
"dividend": 357,
"divisor": 48,
"remainder": 21,
"description": "Let b be the remainder when x - k + 390 is divided by 48."
},
{
"variable": "j",
"dividend": 209,
"divisor": 90,
"remainder": 29,
"description": "Let j be the remainder when x - k + 242 is divided by 90."
},
{
"variable": "u",
"dividend": 923,
"divisor": 48,
"remainder": 11,
"description": "Let u be the remainder when x - k + 956 is divided by 48."
},
{
"variable": "o",
"dividend": 717,
"divisor": 66,
"remainder": 57,
"description": "Let o be the remainder when b - u - j + 736 is divided by 66."
}
],
"final_dividend": 305,
"final_remainder": 11,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let u be the remainder when 936 is divided by 45. Let y be the remainder when 216 is divided by 56. Let r be the remainder when 706 is divided by 35. Let m be the remainder when u - y - r + 934 is divided by 33. Let p be the remainder when y - r - u + 341 is divided by 98. Let s be the remainder when y - r - u + 706 is divided by 94. Let g be the remainder when u - r + y + 133 is divided by 84. Let v be the remainder when u + y - r + 792 is divided by 94. Let n be the remainder when s + p - g - v - m + 559 is divided by 65. Let c be the remainder when p - s + v + g - m + 378 is divided by 54. What is the remainder when n - c + 443 is divided by 53?
Please reason step by step, and put your final answer within \boxed{}.
|
32
| 46
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2, 3 -> 4, 5, 6, 7, 8 -> 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "u",
"dividend": 936,
"divisor": 45,
"remainder": 36,
"description": "Let u be the remainder when 936 is divided by 45."
},
{
"variable": "y",
"dividend": 216,
"divisor": 56,
"remainder": 48,
"description": "Let y be the remainder when 216 is divided by 56."
},
{
"variable": "r",
"dividend": 706,
"divisor": 35,
"remainder": 6,
"description": "Let r be the remainder when 706 is divided by 35."
},
{
"variable": "m",
"dividend": 916,
"divisor": 33,
"remainder": 25,
"description": "Let m be the remainder when u - y - r + 934 is divided by 33."
},
{
"variable": "p",
"dividend": 347,
"divisor": 98,
"remainder": 53,
"description": "Let p be the remainder when y - r - u + 341 is divided by 98."
},
{
"variable": "s",
"dividend": 712,
"divisor": 94,
"remainder": 54,
"description": "Let s be the remainder when y - r - u + 706 is divided by 94."
},
{
"variable": "g",
"dividend": 211,
"divisor": 84,
"remainder": 43,
"description": "Let g be the remainder when u - r + y + 133 is divided by 84."
},
{
"variable": "v",
"dividend": 870,
"divisor": 94,
"remainder": 24,
"description": "Let v be the remainder when u + y - r + 792 is divided by 94."
},
{
"variable": "n",
"dividend": 574,
"divisor": 65,
"remainder": 54,
"description": "Let n be the remainder when s + p - g - v - m + 559 is divided by 65."
},
{
"variable": "c",
"dividend": 419,
"divisor": 54,
"remainder": 41,
"description": "Let c be the remainder when p - s + v + g - m + 378 is divided by 54."
}
],
"final_dividend": 456,
"final_remainder": 32,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let d be the remainder when 763 is divided by 53. Let v be the remainder when 919 is divided by 96. Let b be the remainder when v - d + 639 is divided by 41. Let w be the remainder when d - v + 324 is divided by 69. Let f be the remainder when v - d + 821 is divided by 94. Let n be the remainder when d - v + 855 is divided by 35. Let q be the remainder when w + b - n - f + 295 is divided by 36. Let z be the remainder when f - w - n - b + 494 is divided by 24. Let m be the remainder when q - z + 775 is divided by 68. Let c be the remainder when m + 180 is divided by 50. What is the remainder when c + 392 is divided by 40?
Please reason step by step, and put your final answer within \boxed{}.
|
12
| 47
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2 -> 3, 4, 5, 6 -> 7, 8 -> 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "d",
"dividend": 763,
"divisor": 53,
"remainder": 21,
"description": "Let d be the remainder when 763 is divided by 53."
},
{
"variable": "v",
"dividend": 919,
"divisor": 96,
"remainder": 55,
"description": "Let v be the remainder when 919 is divided by 96."
},
{
"variable": "b",
"dividend": 673,
"divisor": 41,
"remainder": 17,
"description": "Let b be the remainder when v - d + 639 is divided by 41."
},
{
"variable": "w",
"dividend": 290,
"divisor": 69,
"remainder": 14,
"description": "Let w be the remainder when d - v + 324 is divided by 69."
},
{
"variable": "f",
"dividend": 855,
"divisor": 94,
"remainder": 9,
"description": "Let f be the remainder when v - d + 821 is divided by 94."
},
{
"variable": "n",
"dividend": 821,
"divisor": 35,
"remainder": 16,
"description": "Let n be the remainder when d - v + 855 is divided by 35."
},
{
"variable": "q",
"dividend": 301,
"divisor": 36,
"remainder": 13,
"description": "Let q be the remainder when w + b - n - f + 295 is divided by 36."
},
{
"variable": "z",
"dividend": 456,
"divisor": 24,
"remainder": 0,
"description": "Let z be the remainder when f - w - n - b + 494 is divided by 24."
},
{
"variable": "m",
"dividend": 788,
"divisor": 68,
"remainder": 40,
"description": "Let m be the remainder when q - z + 775 is divided by 68."
},
{
"variable": "c",
"dividend": 220,
"divisor": 50,
"remainder": 20,
"description": "Let c be the remainder when m + 180 is divided by 50."
}
],
"final_dividend": 412,
"final_remainder": 12,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let t be the remainder when 750 is divided by 72. Let x be the remainder when t + 730 is divided by 98. Let k be the remainder when x + 196 is divided by 81. Let a be the remainder when x + 169 is divided by 46. Let b be the remainder when k - a + 95 is divided by 50. Let r be the remainder when k - a + 787 is divided by 27. Let w be the remainder when a - k + 198 is divided by 63. Let d be the remainder when b - w - r + 339 is divided by 38. Let n be the remainder when b + r - w + 924 is divided by 82. Let m be the remainder when w - r + b + 804 is divided by 79. What is the remainder when m - n - d + 472 is divided by 93?
Please reason step by step, and put your final answer within \boxed{}.
|
84
| 48
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3, 4 -> 5, 6, 7 -> 8, 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "t",
"dividend": 750,
"divisor": 72,
"remainder": 30,
"description": "Let t be the remainder when 750 is divided by 72."
},
{
"variable": "x",
"dividend": 760,
"divisor": 98,
"remainder": 74,
"description": "Let x be the remainder when t + 730 is divided by 98."
},
{
"variable": "k",
"dividend": 270,
"divisor": 81,
"remainder": 27,
"description": "Let k be the remainder when x + 196 is divided by 81."
},
{
"variable": "a",
"dividend": 243,
"divisor": 46,
"remainder": 13,
"description": "Let a be the remainder when x + 169 is divided by 46."
},
{
"variable": "b",
"dividend": 109,
"divisor": 50,
"remainder": 9,
"description": "Let b be the remainder when k - a + 95 is divided by 50."
},
{
"variable": "r",
"dividend": 801,
"divisor": 27,
"remainder": 18,
"description": "Let r be the remainder when k - a + 787 is divided by 27."
},
{
"variable": "w",
"dividend": 184,
"divisor": 63,
"remainder": 58,
"description": "Let w be the remainder when a - k + 198 is divided by 63."
},
{
"variable": "d",
"dividend": 272,
"divisor": 38,
"remainder": 6,
"description": "Let d be the remainder when b - w - r + 339 is divided by 38."
},
{
"variable": "n",
"dividend": 893,
"divisor": 82,
"remainder": 73,
"description": "Let n be the remainder when b + r - w + 924 is divided by 82."
},
{
"variable": "m",
"dividend": 853,
"divisor": 79,
"remainder": 63,
"description": "Let m be the remainder when w - r + b + 804 is divided by 79."
}
],
"final_dividend": 456,
"final_remainder": 84,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let k be the remainder when 924 is divided by 36. Let i be the remainder when k + 435 is divided by 82. Let m be the remainder when k + 687 is divided by 45. Let r be the remainder when m - i + 991 is divided by 31. Let x be the remainder when r + 917 is divided by 96. Let v be the remainder when x + 798 is divided by 27. Let d be the remainder when x + 313 is divided by 17. Let u be the remainder when x + 916 is divided by 99. Let y be the remainder when u - d - v + 163 is divided by 41. Let a be the remainder when y + 484 is divided by 90. What is the remainder when a + 488 is divided by 58?
Please reason step by step, and put your final answer within \boxed{}.
|
40
| 49
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2, 3 -> 4 -> 5 -> 6, 7, 8 -> 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "k",
"dividend": 924,
"divisor": 36,
"remainder": 24,
"description": "Let k be the remainder when 924 is divided by 36."
},
{
"variable": "i",
"dividend": 459,
"divisor": 82,
"remainder": 49,
"description": "Let i be the remainder when k + 435 is divided by 82."
},
{
"variable": "m",
"dividend": 711,
"divisor": 45,
"remainder": 36,
"description": "Let m be the remainder when k + 687 is divided by 45."
},
{
"variable": "r",
"dividend": 978,
"divisor": 31,
"remainder": 17,
"description": "Let r be the remainder when m - i + 991 is divided by 31."
},
{
"variable": "x",
"dividend": 934,
"divisor": 96,
"remainder": 70,
"description": "Let x be the remainder when r + 917 is divided by 96."
},
{
"variable": "v",
"dividend": 868,
"divisor": 27,
"remainder": 4,
"description": "Let v be the remainder when x + 798 is divided by 27."
},
{
"variable": "d",
"dividend": 383,
"divisor": 17,
"remainder": 9,
"description": "Let d be the remainder when x + 313 is divided by 17."
},
{
"variable": "u",
"dividend": 986,
"divisor": 99,
"remainder": 95,
"description": "Let u be the remainder when x + 916 is divided by 99."
},
{
"variable": "y",
"dividend": 245,
"divisor": 41,
"remainder": 40,
"description": "Let y be the remainder when u - d - v + 163 is divided by 41."
},
{
"variable": "a",
"dividend": 524,
"divisor": 90,
"remainder": 74,
"description": "Let a be the remainder when y + 484 is divided by 90."
}
],
"final_dividend": 562,
"final_remainder": 40,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let f be the remainder when 848 is divided by 21. Let g be the remainder when f + 772 is divided by 91. Let n be the remainder when g + 918 is divided by 55. Let l be the remainder when g + 455 is divided by 78. Let b be the remainder when g + 892 is divided by 64. Let s be the remainder when g + 322 is divided by 73. Let a be the remainder when g + 393 is divided by 46. Let k be the remainder when g + 181 is divided by 83. Let z be the remainder when g + 746 is divided by 53. Let p be the remainder when a - b - l - z + s + k - n + 280 is divided by 15. What is the remainder when p + 188 is divided by 45?
Please reason step by step, and put your final answer within \boxed{}.
|
15
| 50
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3, 4, 5, 6, 7, 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "f",
"dividend": 848,
"divisor": 21,
"remainder": 8,
"description": "Let f be the remainder when 848 is divided by 21."
},
{
"variable": "g",
"dividend": 780,
"divisor": 91,
"remainder": 52,
"description": "Let g be the remainder when f + 772 is divided by 91."
},
{
"variable": "n",
"dividend": 970,
"divisor": 55,
"remainder": 35,
"description": "Let n be the remainder when g + 918 is divided by 55."
},
{
"variable": "l",
"dividend": 507,
"divisor": 78,
"remainder": 39,
"description": "Let l be the remainder when g + 455 is divided by 78."
},
{
"variable": "b",
"dividend": 944,
"divisor": 64,
"remainder": 48,
"description": "Let b be the remainder when g + 892 is divided by 64."
},
{
"variable": "s",
"dividend": 374,
"divisor": 73,
"remainder": 9,
"description": "Let s be the remainder when g + 322 is divided by 73."
},
{
"variable": "a",
"dividend": 445,
"divisor": 46,
"remainder": 31,
"description": "Let a be the remainder when g + 393 is divided by 46."
},
{
"variable": "k",
"dividend": 233,
"divisor": 83,
"remainder": 67,
"description": "Let k be the remainder when g + 181 is divided by 83."
},
{
"variable": "z",
"dividend": 798,
"divisor": 53,
"remainder": 3,
"description": "Let z be the remainder when g + 746 is divided by 53."
},
{
"variable": "p",
"dividend": 262,
"divisor": 15,
"remainder": 7,
"description": "Let p be the remainder when a - b - l - z + s + k - n + 280 is divided by 15."
}
],
"final_dividend": 195,
"final_remainder": 15,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let y be the remainder when 193 is divided by 93. Let n be the remainder when 101 is divided by 22. Let k be the remainder when 179 is divided by 71. Let v be the remainder when k + n - y + 893 is divided by 85. Let h be the remainder when y - n + k + 461 is divided by 64. Let l be the remainder when v - h + 283 is divided by 23. Let d be the remainder when l + 746 is divided by 27. Let u be the remainder when l + 633 is divided by 18. Let p be the remainder when l + 755 is divided by 88. Let w be the remainder when p - d - u + 932 is divided by 66. What is the remainder when w + 132 is divided by 37?
Please reason step by step, and put your final answer within \boxed{}.
|
3
| 51
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2, 3 -> 4, 5 -> 6 -> 7, 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "y",
"dividend": 193,
"divisor": 93,
"remainder": 7,
"description": "Let y be the remainder when 193 is divided by 93."
},
{
"variable": "n",
"dividend": 101,
"divisor": 22,
"remainder": 13,
"description": "Let n be the remainder when 101 is divided by 22."
},
{
"variable": "k",
"dividend": 179,
"divisor": 71,
"remainder": 37,
"description": "Let k be the remainder when 179 is divided by 71."
},
{
"variable": "v",
"dividend": 936,
"divisor": 85,
"remainder": 1,
"description": "Let v be the remainder when k + n - y + 893 is divided by 85."
},
{
"variable": "h",
"dividend": 492,
"divisor": 64,
"remainder": 44,
"description": "Let h be the remainder when y - n + k + 461 is divided by 64."
},
{
"variable": "l",
"dividend": 240,
"divisor": 23,
"remainder": 10,
"description": "Let l be the remainder when v - h + 283 is divided by 23."
},
{
"variable": "d",
"dividend": 756,
"divisor": 27,
"remainder": 0,
"description": "Let d be the remainder when l + 746 is divided by 27."
},
{
"variable": "u",
"dividend": 643,
"divisor": 18,
"remainder": 13,
"description": "Let u be the remainder when l + 633 is divided by 18."
},
{
"variable": "p",
"dividend": 765,
"divisor": 88,
"remainder": 61,
"description": "Let p be the remainder when l + 755 is divided by 88."
},
{
"variable": "w",
"dividend": 980,
"divisor": 66,
"remainder": 56,
"description": "Let w be the remainder when p - d - u + 932 is divided by 66."
}
],
"final_dividend": 188,
"final_remainder": 3,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let s be the remainder when 186 is divided by 92. Let b be the remainder when s + 713 is divided by 80. Let o be the remainder when b + 316 is divided by 87. Let d be the remainder when o + 953 is divided by 94. Let u be the remainder when o + 587 is divided by 36. Let f be the remainder when o + 250 is divided by 75. Let z be the remainder when o + 718 is divided by 47. Let q be the remainder when o + 563 is divided by 40. Let m be the remainder when q - d - f + z - u + 1108 is divided by 24. Let t be the remainder when m + 638 is divided by 56. What is the remainder when t + 233 is divided by 97?
Please reason step by step, and put your final answer within \boxed{}.
|
82
| 52
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3 -> 4, 5, 6, 7, 8 -> 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "s",
"dividend": 186,
"divisor": 92,
"remainder": 2,
"description": "Let s be the remainder when 186 is divided by 92."
},
{
"variable": "b",
"dividend": 715,
"divisor": 80,
"remainder": 75,
"description": "Let b be the remainder when s + 713 is divided by 80."
},
{
"variable": "o",
"dividend": 391,
"divisor": 87,
"remainder": 43,
"description": "Let o be the remainder when b + 316 is divided by 87."
},
{
"variable": "d",
"dividend": 996,
"divisor": 94,
"remainder": 56,
"description": "Let d be the remainder when o + 953 is divided by 94."
},
{
"variable": "u",
"dividend": 630,
"divisor": 36,
"remainder": 18,
"description": "Let u be the remainder when o + 587 is divided by 36."
},
{
"variable": "f",
"dividend": 293,
"divisor": 75,
"remainder": 68,
"description": "Let f be the remainder when o + 250 is divided by 75."
},
{
"variable": "z",
"dividend": 761,
"divisor": 47,
"remainder": 9,
"description": "Let z be the remainder when o + 718 is divided by 47."
},
{
"variable": "q",
"dividend": 606,
"divisor": 40,
"remainder": 6,
"description": "Let q be the remainder when o + 563 is divided by 40."
},
{
"variable": "m",
"dividend": 981,
"divisor": 24,
"remainder": 21,
"description": "Let m be the remainder when q - d - f + z - u + 1108 is divided by 24."
},
{
"variable": "t",
"dividend": 659,
"divisor": 56,
"remainder": 43,
"description": "Let t be the remainder when m + 638 is divided by 56."
}
],
"final_dividend": 276,
"final_remainder": 82,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let u be the remainder when 393 is divided by 74. Let o be the remainder when 885 is divided by 74. Let g be the remainder when u - o + 233 is divided by 64. Let p be the remainder when g + 566 is divided by 20. Let k be the remainder when p + 646 is divided by 29. Let y be the remainder when k + 689 is divided by 60. Let h be the remainder when k + 804 is divided by 49. Let z be the remainder when h - y + 227 is divided by 40. Let b be the remainder when z + 705 is divided by 88. Let q be the remainder when b + 763 is divided by 49. What is the remainder when q + 811 is divided by 94?
Please reason step by step, and put your final answer within \boxed{}.
|
12
| 53
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2 -> 3 -> 4 -> 5 -> 6, 7 -> 8 -> 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "u",
"dividend": 393,
"divisor": 74,
"remainder": 23,
"description": "Let u be the remainder when 393 is divided by 74."
},
{
"variable": "o",
"dividend": 885,
"divisor": 74,
"remainder": 71,
"description": "Let o be the remainder when 885 is divided by 74."
},
{
"variable": "g",
"dividend": 185,
"divisor": 64,
"remainder": 57,
"description": "Let g be the remainder when u - o + 233 is divided by 64."
},
{
"variable": "p",
"dividend": 623,
"divisor": 20,
"remainder": 3,
"description": "Let p be the remainder when g + 566 is divided by 20."
},
{
"variable": "k",
"dividend": 649,
"divisor": 29,
"remainder": 11,
"description": "Let k be the remainder when p + 646 is divided by 29."
},
{
"variable": "y",
"dividend": 700,
"divisor": 60,
"remainder": 40,
"description": "Let y be the remainder when k + 689 is divided by 60."
},
{
"variable": "h",
"dividend": 815,
"divisor": 49,
"remainder": 31,
"description": "Let h be the remainder when k + 804 is divided by 49."
},
{
"variable": "z",
"dividend": 218,
"divisor": 40,
"remainder": 18,
"description": "Let z be the remainder when h - y + 227 is divided by 40."
},
{
"variable": "b",
"dividend": 723,
"divisor": 88,
"remainder": 19,
"description": "Let b be the remainder when z + 705 is divided by 88."
},
{
"variable": "q",
"dividend": 782,
"divisor": 49,
"remainder": 47,
"description": "Let q be the remainder when b + 763 is divided by 49."
}
],
"final_dividend": 858,
"final_remainder": 12,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let t be the remainder when 229 is divided by 57. Let f be the remainder when t + 849 is divided by 44. Let h be the remainder when f + 429 is divided by 13. Let j be the remainder when h + 635 is divided by 44. Let l be the remainder when j + 809 is divided by 43. Let z be the remainder when l + 166 is divided by 90. Let w be the remainder when z + 535 is divided by 68. Let m be the remainder when z + 523 is divided by 17. Let u be the remainder when z + 173 is divided by 57. Let a be the remainder when z + 599 is divided by 23. What is the remainder when m + u + a - w + 414 is divided by 96?
Please reason step by step, and put your final answer within \boxed{}.
|
88
| 54
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7, 8, 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "t",
"dividend": 229,
"divisor": 57,
"remainder": 1,
"description": "Let t be the remainder when 229 is divided by 57."
},
{
"variable": "f",
"dividend": 850,
"divisor": 44,
"remainder": 14,
"description": "Let f be the remainder when t + 849 is divided by 44."
},
{
"variable": "h",
"dividend": 443,
"divisor": 13,
"remainder": 1,
"description": "Let h be the remainder when f + 429 is divided by 13."
},
{
"variable": "j",
"dividend": 636,
"divisor": 44,
"remainder": 20,
"description": "Let j be the remainder when h + 635 is divided by 44."
},
{
"variable": "l",
"dividend": 829,
"divisor": 43,
"remainder": 12,
"description": "Let l be the remainder when j + 809 is divided by 43."
},
{
"variable": "z",
"dividend": 178,
"divisor": 90,
"remainder": 88,
"description": "Let z be the remainder when l + 166 is divided by 90."
},
{
"variable": "w",
"dividend": 623,
"divisor": 68,
"remainder": 11,
"description": "Let w be the remainder when z + 535 is divided by 68."
},
{
"variable": "m",
"dividend": 611,
"divisor": 17,
"remainder": 16,
"description": "Let m be the remainder when z + 523 is divided by 17."
},
{
"variable": "u",
"dividend": 261,
"divisor": 57,
"remainder": 33,
"description": "Let u be the remainder when z + 173 is divided by 57."
},
{
"variable": "a",
"dividend": 687,
"divisor": 23,
"remainder": 20,
"description": "Let a be the remainder when z + 599 is divided by 23."
}
],
"final_dividend": 472,
"final_remainder": 88,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let n be the remainder when 377 is divided by 50. Let l be the remainder when 481 is divided by 83. Let v be the remainder when n - l + 549 is divided by 74. Let h be the remainder when v + 920 is divided by 69. Let u be the remainder when h + 415 is divided by 49. Let t be the remainder when h + 547 is divided by 80. Let i be the remainder when t - u + 611 is divided by 57. Let r be the remainder when t - u + 142 is divided by 85. Let k be the remainder when i - r + 459 is divided by 13. Let d be the remainder when r - i + 294 is divided by 94. What is the remainder when d - k + 218 is divided by 77?
Please reason step by step, and put your final answer within \boxed{}.
|
14
| 55
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2 -> 3 -> 4 -> 5, 6 -> 7, 8 -> 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "n",
"dividend": 377,
"divisor": 50,
"remainder": 27,
"description": "Let n be the remainder when 377 is divided by 50."
},
{
"variable": "l",
"dividend": 481,
"divisor": 83,
"remainder": 66,
"description": "Let l be the remainder when 481 is divided by 83."
},
{
"variable": "v",
"dividend": 510,
"divisor": 74,
"remainder": 66,
"description": "Let v be the remainder when n - l + 549 is divided by 74."
},
{
"variable": "h",
"dividend": 986,
"divisor": 69,
"remainder": 20,
"description": "Let h be the remainder when v + 920 is divided by 69."
},
{
"variable": "u",
"dividend": 435,
"divisor": 49,
"remainder": 43,
"description": "Let u be the remainder when h + 415 is divided by 49."
},
{
"variable": "t",
"dividend": 567,
"divisor": 80,
"remainder": 7,
"description": "Let t be the remainder when h + 547 is divided by 80."
},
{
"variable": "i",
"dividend": 575,
"divisor": 57,
"remainder": 5,
"description": "Let i be the remainder when t - u + 611 is divided by 57."
},
{
"variable": "r",
"dividend": 106,
"divisor": 85,
"remainder": 21,
"description": "Let r be the remainder when t - u + 142 is divided by 85."
},
{
"variable": "k",
"dividend": 443,
"divisor": 13,
"remainder": 1,
"description": "Let k be the remainder when i - r + 459 is divided by 13."
},
{
"variable": "d",
"dividend": 310,
"divisor": 94,
"remainder": 28,
"description": "Let d be the remainder when r - i + 294 is divided by 94."
}
],
"final_dividend": 245,
"final_remainder": 14,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let w be the remainder when 752 is divided by 27. Let u be the remainder when 706 is divided by 19. Let r be the remainder when w - u + 347 is divided by 17. Let q be the remainder when r + 807 is divided by 60. Let c be the remainder when q + 526 is divided by 50. Let s be the remainder when q + 139 is divided by 39. Let y be the remainder when q + 861 is divided by 27. Let l be the remainder when q + 171 is divided by 29. Let j be the remainder when c - y + s - l + 394 is divided by 67. Let b be the remainder when j + 959 is divided by 43. What is the remainder when b + 166 is divided by 25?
Please reason step by step, and put your final answer within \boxed{}.
|
17
| 56
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2 -> 3 -> 4 -> 5, 6, 7, 8 -> 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "w",
"dividend": 752,
"divisor": 27,
"remainder": 23,
"description": "Let w be the remainder when 752 is divided by 27."
},
{
"variable": "u",
"dividend": 706,
"divisor": 19,
"remainder": 3,
"description": "Let u be the remainder when 706 is divided by 19."
},
{
"variable": "r",
"dividend": 367,
"divisor": 17,
"remainder": 10,
"description": "Let r be the remainder when w - u + 347 is divided by 17."
},
{
"variable": "q",
"dividend": 817,
"divisor": 60,
"remainder": 37,
"description": "Let q be the remainder when r + 807 is divided by 60."
},
{
"variable": "c",
"dividend": 563,
"divisor": 50,
"remainder": 13,
"description": "Let c be the remainder when q + 526 is divided by 50."
},
{
"variable": "s",
"dividend": 176,
"divisor": 39,
"remainder": 20,
"description": "Let s be the remainder when q + 139 is divided by 39."
},
{
"variable": "y",
"dividend": 898,
"divisor": 27,
"remainder": 7,
"description": "Let y be the remainder when q + 861 is divided by 27."
},
{
"variable": "l",
"dividend": 208,
"divisor": 29,
"remainder": 5,
"description": "Let l be the remainder when q + 171 is divided by 29."
},
{
"variable": "j",
"dividend": 415,
"divisor": 67,
"remainder": 13,
"description": "Let j be the remainder when c - y + s - l + 394 is divided by 67."
},
{
"variable": "b",
"dividend": 972,
"divisor": 43,
"remainder": 26,
"description": "Let b be the remainder when j + 959 is divided by 43."
}
],
"final_dividend": 192,
"final_remainder": 17,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let u be the remainder when 150 is divided by 75. Let z be the remainder when u + 366 is divided by 48. Let t be the remainder when u + 514 is divided by 13. Let w be the remainder when t - z + 227 is divided by 81. Let v be the remainder when w + 70 is divided by 25. Let i be the remainder when w + 191 is divided by 38. Let y be the remainder when v - i + 925 is divided by 61. Let q be the remainder when y + 149 is divided by 12. Let j be the remainder when q + 544 is divided by 92. Let g be the remainder when q + 957 is divided by 21. What is the remainder when g - j + 152 is divided by 52?
Please reason step by step, and put your final answer within \boxed{}.
|
47
| 57
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2, 3 -> 4 -> 5, 6 -> 7 -> 8 -> 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "u",
"dividend": 150,
"divisor": 75,
"remainder": 0,
"description": "Let u be the remainder when 150 is divided by 75."
},
{
"variable": "z",
"dividend": 366,
"divisor": 48,
"remainder": 30,
"description": "Let z be the remainder when u + 366 is divided by 48."
},
{
"variable": "t",
"dividend": 514,
"divisor": 13,
"remainder": 7,
"description": "Let t be the remainder when u + 514 is divided by 13."
},
{
"variable": "w",
"dividend": 204,
"divisor": 81,
"remainder": 42,
"description": "Let w be the remainder when t - z + 227 is divided by 81."
},
{
"variable": "v",
"dividend": 112,
"divisor": 25,
"remainder": 12,
"description": "Let v be the remainder when w + 70 is divided by 25."
},
{
"variable": "i",
"dividend": 233,
"divisor": 38,
"remainder": 5,
"description": "Let i be the remainder when w + 191 is divided by 38."
},
{
"variable": "y",
"dividend": 932,
"divisor": 61,
"remainder": 17,
"description": "Let y be the remainder when v - i + 925 is divided by 61."
},
{
"variable": "q",
"dividend": 166,
"divisor": 12,
"remainder": 10,
"description": "Let q be the remainder when y + 149 is divided by 12."
},
{
"variable": "j",
"dividend": 554,
"divisor": 92,
"remainder": 2,
"description": "Let j be the remainder when q + 544 is divided by 92."
},
{
"variable": "g",
"dividend": 967,
"divisor": 21,
"remainder": 1,
"description": "Let g be the remainder when q + 957 is divided by 21."
}
],
"final_dividend": 151,
"final_remainder": 47,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let k be the remainder when 381 is divided by 33. Let p be the remainder when k + 234 is divided by 67. Let i be the remainder when k + 716 is divided by 88. Let z be the remainder when k + 744 is divided by 41. Let u be the remainder when k + 503 is divided by 73. Let o be the remainder when i - z - u + p + 711 is divided by 71. Let r be the remainder when p - z - i - u + 389 is divided by 41. Let g be the remainder when i - p + u - z + 677 is divided by 13. Let m be the remainder when r - g + o + 596 is divided by 84. Let q be the remainder when r - o + g + 378 is divided by 38. What is the remainder when q - m + 878 is divided by 85?
Please reason step by step, and put your final answer within \boxed{}.
|
55
| 58
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2, 3, 4, 5 -> 6, 7, 8 -> 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "k",
"dividend": 381,
"divisor": 33,
"remainder": 18,
"description": "Let k be the remainder when 381 is divided by 33."
},
{
"variable": "p",
"dividend": 252,
"divisor": 67,
"remainder": 51,
"description": "Let p be the remainder when k + 234 is divided by 67."
},
{
"variable": "i",
"dividend": 734,
"divisor": 88,
"remainder": 30,
"description": "Let i be the remainder when k + 716 is divided by 88."
},
{
"variable": "z",
"dividend": 762,
"divisor": 41,
"remainder": 24,
"description": "Let z be the remainder when k + 744 is divided by 41."
},
{
"variable": "u",
"dividend": 521,
"divisor": 73,
"remainder": 10,
"description": "Let u be the remainder when k + 503 is divided by 73."
},
{
"variable": "o",
"dividend": 758,
"divisor": 71,
"remainder": 48,
"description": "Let o be the remainder when i - z - u + p + 711 is divided by 71."
},
{
"variable": "r",
"dividend": 376,
"divisor": 41,
"remainder": 7,
"description": "Let r be the remainder when p - z - i - u + 389 is divided by 41."
},
{
"variable": "g",
"dividend": 642,
"divisor": 13,
"remainder": 5,
"description": "Let g be the remainder when i - p + u - z + 677 is divided by 13."
},
{
"variable": "m",
"dividend": 646,
"divisor": 84,
"remainder": 58,
"description": "Let m be the remainder when r - g + o + 596 is divided by 84."
},
{
"variable": "q",
"dividend": 342,
"divisor": 38,
"remainder": 0,
"description": "Let q be the remainder when r - o + g + 378 is divided by 38."
}
],
"final_dividend": 820,
"final_remainder": 55,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let i be the remainder when 716 is divided by 39. Let s be the remainder when 639 is divided by 12. Let a be the remainder when i - s + 823 is divided by 10. Let k be the remainder when a + 156 is divided by 51. Let d be the remainder when a + 696 is divided by 28. Let b be the remainder when a + 962 is divided by 24. Let r be the remainder when d - b - k + 422 is divided by 56. Let w be the remainder when k - d - b + 823 is divided by 27. Let m be the remainder when r - w + 227 is divided by 38. Let y be the remainder when m + 816 is divided by 10. What is the remainder when y + 492 is divided by 83?
Please reason step by step, and put your final answer within \boxed{}.
|
2
| 59
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2 -> 3 -> 4, 5, 6 -> 7, 8 -> 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "i",
"dividend": 716,
"divisor": 39,
"remainder": 14,
"description": "Let i be the remainder when 716 is divided by 39."
},
{
"variable": "s",
"dividend": 639,
"divisor": 12,
"remainder": 3,
"description": "Let s be the remainder when 639 is divided by 12."
},
{
"variable": "a",
"dividend": 834,
"divisor": 10,
"remainder": 4,
"description": "Let a be the remainder when i - s + 823 is divided by 10."
},
{
"variable": "k",
"dividend": 160,
"divisor": 51,
"remainder": 7,
"description": "Let k be the remainder when a + 156 is divided by 51."
},
{
"variable": "d",
"dividend": 700,
"divisor": 28,
"remainder": 0,
"description": "Let d be the remainder when a + 696 is divided by 28."
},
{
"variable": "b",
"dividend": 966,
"divisor": 24,
"remainder": 6,
"description": "Let b be the remainder when a + 962 is divided by 24."
},
{
"variable": "r",
"dividend": 409,
"divisor": 56,
"remainder": 17,
"description": "Let r be the remainder when d - b - k + 422 is divided by 56."
},
{
"variable": "w",
"dividend": 824,
"divisor": 27,
"remainder": 14,
"description": "Let w be the remainder when k - d - b + 823 is divided by 27."
},
{
"variable": "m",
"dividend": 230,
"divisor": 38,
"remainder": 2,
"description": "Let m be the remainder when r - w + 227 is divided by 38."
},
{
"variable": "y",
"dividend": 818,
"divisor": 10,
"remainder": 8,
"description": "Let y be the remainder when m + 816 is divided by 10."
}
],
"final_dividend": 500,
"final_remainder": 2,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let b be the remainder when 427 is divided by 54. Let t be the remainder when b + 141 is divided by 91. Let f be the remainder when t + 746 is divided by 95. Let u be the remainder when t + 103 is divided by 67. Let q be the remainder when u - f + 407 is divided by 36. Let h be the remainder when q + 147 is divided by 10. Let d be the remainder when q + 848 is divided by 66. Let o be the remainder when d - h + 610 is divided by 31. Let r be the remainder when h - d + 224 is divided by 22. Let y be the remainder when r - o + 162 is divided by 47. What is the remainder when y + 240 is divided by 53?
Please reason step by step, and put your final answer within \boxed{}.
|
9
| 60
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3, 4 -> 5 -> 6, 7 -> 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "b",
"dividend": 427,
"divisor": 54,
"remainder": 49,
"description": "Let b be the remainder when 427 is divided by 54."
},
{
"variable": "t",
"dividend": 190,
"divisor": 91,
"remainder": 8,
"description": "Let t be the remainder when b + 141 is divided by 91."
},
{
"variable": "f",
"dividend": 754,
"divisor": 95,
"remainder": 89,
"description": "Let f be the remainder when t + 746 is divided by 95."
},
{
"variable": "u",
"dividend": 111,
"divisor": 67,
"remainder": 44,
"description": "Let u be the remainder when t + 103 is divided by 67."
},
{
"variable": "q",
"dividend": 362,
"divisor": 36,
"remainder": 2,
"description": "Let q be the remainder when u - f + 407 is divided by 36."
},
{
"variable": "h",
"dividend": 149,
"divisor": 10,
"remainder": 9,
"description": "Let h be the remainder when q + 147 is divided by 10."
},
{
"variable": "d",
"dividend": 850,
"divisor": 66,
"remainder": 58,
"description": "Let d be the remainder when q + 848 is divided by 66."
},
{
"variable": "o",
"dividend": 659,
"divisor": 31,
"remainder": 8,
"description": "Let o be the remainder when d - h + 610 is divided by 31."
},
{
"variable": "r",
"dividend": 175,
"divisor": 22,
"remainder": 21,
"description": "Let r be the remainder when h - d + 224 is divided by 22."
},
{
"variable": "y",
"dividend": 175,
"divisor": 47,
"remainder": 34,
"description": "Let y be the remainder when r - o + 162 is divided by 47."
}
],
"final_dividend": 274,
"final_remainder": 9,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let m be the remainder when 260 is divided by 65. Let i be the remainder when 439 is divided by 22. Let b be the remainder when i - m + 322 is divided by 34. Let v be the remainder when b + 499 is divided by 16. Let z be the remainder when v + 954 is divided by 80. Let x be the remainder when v + 149 is divided by 29. Let o be the remainder when v + 531 is divided by 10. Let q be the remainder when x - z + o + 257 is divided by 47. Let w be the remainder when z - o - x + 793 is divided by 20. Let j be the remainder when q - w + 467 is divided by 21. What is the remainder when j + 284 is divided by 57?
Please reason step by step, and put your final answer within \boxed{}.
|
6
| 61
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2 -> 3 -> 4 -> 5, 6, 7 -> 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "m",
"dividend": 260,
"divisor": 65,
"remainder": 0,
"description": "Let m be the remainder when 260 is divided by 65."
},
{
"variable": "i",
"dividend": 439,
"divisor": 22,
"remainder": 21,
"description": "Let i be the remainder when 439 is divided by 22."
},
{
"variable": "b",
"dividend": 343,
"divisor": 34,
"remainder": 3,
"description": "Let b be the remainder when i - m + 322 is divided by 34."
},
{
"variable": "v",
"dividend": 502,
"divisor": 16,
"remainder": 6,
"description": "Let v be the remainder when b + 499 is divided by 16."
},
{
"variable": "z",
"dividend": 960,
"divisor": 80,
"remainder": 0,
"description": "Let z be the remainder when v + 954 is divided by 80."
},
{
"variable": "x",
"dividend": 155,
"divisor": 29,
"remainder": 10,
"description": "Let x be the remainder when v + 149 is divided by 29."
},
{
"variable": "o",
"dividend": 537,
"divisor": 10,
"remainder": 7,
"description": "Let o be the remainder when v + 531 is divided by 10."
},
{
"variable": "q",
"dividend": 274,
"divisor": 47,
"remainder": 39,
"description": "Let q be the remainder when x - z + o + 257 is divided by 47."
},
{
"variable": "w",
"dividend": 776,
"divisor": 20,
"remainder": 16,
"description": "Let w be the remainder when z - o - x + 793 is divided by 20."
},
{
"variable": "j",
"dividend": 490,
"divisor": 21,
"remainder": 7,
"description": "Let j be the remainder when q - w + 467 is divided by 21."
}
],
"final_dividend": 291,
"final_remainder": 6,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let v be the remainder when 783 is divided by 99. Let h be the remainder when 784 is divided by 20. Let y be the remainder when v - h + 852 is divided by 79. Let m be the remainder when v - h + 320 is divided by 63. Let l be the remainder when h - v + 363 is divided by 60. Let s be the remainder when h - v + 266 is divided by 37. Let b be the remainder when h - v + 275 is divided by 35. Let o be the remainder when y - b + m - l + s + 173 is divided by 81. Let q be the remainder when s - l - m - y - b + 392 is divided by 23. Let a be the remainder when o - q + 497 is divided by 61. What is the remainder when a + 790 is divided by 52?
Please reason step by step, and put your final answer within \boxed{}.
|
27
| 62
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2 -> 3, 4, 5, 6, 7 -> 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "v",
"dividend": 783,
"divisor": 99,
"remainder": 90,
"description": "Let v be the remainder when 783 is divided by 99."
},
{
"variable": "h",
"dividend": 784,
"divisor": 20,
"remainder": 4,
"description": "Let h be the remainder when 784 is divided by 20."
},
{
"variable": "y",
"dividend": 938,
"divisor": 79,
"remainder": 69,
"description": "Let y be the remainder when v - h + 852 is divided by 79."
},
{
"variable": "m",
"dividend": 406,
"divisor": 63,
"remainder": 28,
"description": "Let m be the remainder when v - h + 320 is divided by 63."
},
{
"variable": "l",
"dividend": 277,
"divisor": 60,
"remainder": 37,
"description": "Let l be the remainder when h - v + 363 is divided by 60."
},
{
"variable": "s",
"dividend": 180,
"divisor": 37,
"remainder": 32,
"description": "Let s be the remainder when h - v + 266 is divided by 37."
},
{
"variable": "b",
"dividend": 189,
"divisor": 35,
"remainder": 14,
"description": "Let b be the remainder when h - v + 275 is divided by 35."
},
{
"variable": "o",
"dividend": 251,
"divisor": 81,
"remainder": 8,
"description": "Let o be the remainder when y - b + m - l + s + 173 is divided by 81."
},
{
"variable": "q",
"dividend": 276,
"divisor": 23,
"remainder": 0,
"description": "Let q be the remainder when s - l - m - y - b + 392 is divided by 23."
},
{
"variable": "a",
"dividend": 505,
"divisor": 61,
"remainder": 17,
"description": "Let a be the remainder when o - q + 497 is divided by 61."
}
],
"final_dividend": 807,
"final_remainder": 27,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let s be the remainder when 978 is divided by 72. Let n be the remainder when s + 158 is divided by 97. Let b be the remainder when n + 401 is divided by 27. Let w be the remainder when n + 369 is divided by 51. Let j be the remainder when n + 755 is divided by 87. Let l be the remainder when n + 546 is divided by 34. Let c be the remainder when b + w + j - l + 749 is divided by 62. Let k be the remainder when l - b + j + w + 44 is divided by 61. Let z be the remainder when w - b - l - j + 854 is divided by 16. Let d be the remainder when b - l - w - j + 356 is divided by 40. What is the remainder when d - z + k + c + 932 is divided by 43?
Please reason step by step, and put your final answer within \boxed{}.
|
31
| 63
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3, 4, 5, 6 -> 7, 8, 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "s",
"dividend": 978,
"divisor": 72,
"remainder": 42,
"description": "Let s be the remainder when 978 is divided by 72."
},
{
"variable": "n",
"dividend": 200,
"divisor": 97,
"remainder": 6,
"description": "Let n be the remainder when s + 158 is divided by 97."
},
{
"variable": "b",
"dividend": 407,
"divisor": 27,
"remainder": 2,
"description": "Let b be the remainder when n + 401 is divided by 27."
},
{
"variable": "w",
"dividend": 375,
"divisor": 51,
"remainder": 18,
"description": "Let w be the remainder when n + 369 is divided by 51."
},
{
"variable": "j",
"dividend": 761,
"divisor": 87,
"remainder": 65,
"description": "Let j be the remainder when n + 755 is divided by 87."
},
{
"variable": "l",
"dividend": 552,
"divisor": 34,
"remainder": 8,
"description": "Let l be the remainder when n + 546 is divided by 34."
},
{
"variable": "c",
"dividend": 826,
"divisor": 62,
"remainder": 20,
"description": "Let c be the remainder when b + w + j - l + 749 is divided by 62."
},
{
"variable": "k",
"dividend": 133,
"divisor": 61,
"remainder": 11,
"description": "Let k be the remainder when l - b + j + w + 44 is divided by 61."
},
{
"variable": "z",
"dividend": 797,
"divisor": 16,
"remainder": 13,
"description": "Let z be the remainder when w - b - l - j + 854 is divided by 16."
},
{
"variable": "d",
"dividend": 267,
"divisor": 40,
"remainder": 27,
"description": "Let d be the remainder when b - l - w - j + 356 is divided by 40."
}
],
"final_dividend": 977,
"final_remainder": 31,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let r be the remainder when 715 is divided by 32. Let d be the remainder when r + 347 is divided by 38. Let o be the remainder when d + 813 is divided by 49. Let n be the remainder when o + 488 is divided by 45. Let y be the remainder when o + 525 is divided by 54. Let p be the remainder when o + 532 is divided by 37. Let j be the remainder when n + y - p + 628 is divided by 96. Let a be the remainder when j + 798 is divided by 48. Let l be the remainder when j + 163 is divided by 71. Let z be the remainder when l - a + 301 is divided by 45. What is the remainder when z + 607 is divided by 29?
Please reason step by step, and put your final answer within \boxed{}.
|
20
| 64
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3 -> 4, 5, 6 -> 7 -> 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "r",
"dividend": 715,
"divisor": 32,
"remainder": 11,
"description": "Let r be the remainder when 715 is divided by 32."
},
{
"variable": "d",
"dividend": 358,
"divisor": 38,
"remainder": 16,
"description": "Let d be the remainder when r + 347 is divided by 38."
},
{
"variable": "o",
"dividend": 829,
"divisor": 49,
"remainder": 45,
"description": "Let o be the remainder when d + 813 is divided by 49."
},
{
"variable": "n",
"dividend": 533,
"divisor": 45,
"remainder": 38,
"description": "Let n be the remainder when o + 488 is divided by 45."
},
{
"variable": "y",
"dividend": 570,
"divisor": 54,
"remainder": 30,
"description": "Let y be the remainder when o + 525 is divided by 54."
},
{
"variable": "p",
"dividend": 577,
"divisor": 37,
"remainder": 22,
"description": "Let p be the remainder when o + 532 is divided by 37."
},
{
"variable": "j",
"dividend": 674,
"divisor": 96,
"remainder": 2,
"description": "Let j be the remainder when n + y - p + 628 is divided by 96."
},
{
"variable": "a",
"dividend": 800,
"divisor": 48,
"remainder": 32,
"description": "Let a be the remainder when j + 798 is divided by 48."
},
{
"variable": "l",
"dividend": 165,
"divisor": 71,
"remainder": 23,
"description": "Let l be the remainder when j + 163 is divided by 71."
},
{
"variable": "z",
"dividend": 292,
"divisor": 45,
"remainder": 22,
"description": "Let z be the remainder when l - a + 301 is divided by 45."
}
],
"final_dividend": 629,
"final_remainder": 20,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let y be the remainder when 497 is divided by 61. Let f be the remainder when y + 688 is divided by 14. Let n be the remainder when f + 924 is divided by 83. Let k be the remainder when f + 832 is divided by 53. Let s be the remainder when f + 636 is divided by 97. Let x be the remainder when n + s - k + 160 is divided by 95. Let g be the remainder when x + 849 is divided by 26. Let j be the remainder when x + 872 is divided by 81. Let c be the remainder when x + 434 is divided by 97. Let i be the remainder when x + 454 is divided by 38. What is the remainder when g - i - j - c + 714 is divided by 38?
Please reason step by step, and put your final answer within \boxed{}.
|
11
| 65
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3, 4, 5 -> 6 -> 7, 8, 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "y",
"dividend": 497,
"divisor": 61,
"remainder": 9,
"description": "Let y be the remainder when 497 is divided by 61."
},
{
"variable": "f",
"dividend": 697,
"divisor": 14,
"remainder": 11,
"description": "Let f be the remainder when y + 688 is divided by 14."
},
{
"variable": "n",
"dividend": 935,
"divisor": 83,
"remainder": 22,
"description": "Let n be the remainder when f + 924 is divided by 83."
},
{
"variable": "k",
"dividend": 843,
"divisor": 53,
"remainder": 48,
"description": "Let k be the remainder when f + 832 is divided by 53."
},
{
"variable": "s",
"dividend": 647,
"divisor": 97,
"remainder": 65,
"description": "Let s be the remainder when f + 636 is divided by 97."
},
{
"variable": "x",
"dividend": 199,
"divisor": 95,
"remainder": 9,
"description": "Let x be the remainder when n + s - k + 160 is divided by 95."
},
{
"variable": "g",
"dividend": 858,
"divisor": 26,
"remainder": 0,
"description": "Let g be the remainder when x + 849 is divided by 26."
},
{
"variable": "j",
"dividend": 881,
"divisor": 81,
"remainder": 71,
"description": "Let j be the remainder when x + 872 is divided by 81."
},
{
"variable": "c",
"dividend": 443,
"divisor": 97,
"remainder": 55,
"description": "Let c be the remainder when x + 434 is divided by 97."
},
{
"variable": "i",
"dividend": 463,
"divisor": 38,
"remainder": 7,
"description": "Let i be the remainder when x + 454 is divided by 38."
}
],
"final_dividend": 581,
"final_remainder": 11,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let v be the remainder when 305 is divided by 27. Let c be the remainder when v + 675 is divided by 62. Let w be the remainder when c + 422 is divided by 28. Let k be the remainder when c + 598 is divided by 20. Let y be the remainder when w - k + 120 is divided by 90. Let m be the remainder when y + 300 is divided by 45. Let p be the remainder when y + 868 is divided by 83. Let g be the remainder when y + 890 is divided by 72. Let i be the remainder when y + 715 is divided by 26. Let b be the remainder when p - g - m + i + 677 is divided by 91. What is the remainder when b + 839 is divided by 35?
Please reason step by step, and put your final answer within \boxed{}.
|
8
| 66
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3, 4 -> 5 -> 6, 7, 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "v",
"dividend": 305,
"divisor": 27,
"remainder": 8,
"description": "Let v be the remainder when 305 is divided by 27."
},
{
"variable": "c",
"dividend": 683,
"divisor": 62,
"remainder": 1,
"description": "Let c be the remainder when v + 675 is divided by 62."
},
{
"variable": "w",
"dividend": 423,
"divisor": 28,
"remainder": 3,
"description": "Let w be the remainder when c + 422 is divided by 28."
},
{
"variable": "k",
"dividend": 599,
"divisor": 20,
"remainder": 19,
"description": "Let k be the remainder when c + 598 is divided by 20."
},
{
"variable": "y",
"dividend": 104,
"divisor": 90,
"remainder": 14,
"description": "Let y be the remainder when w - k + 120 is divided by 90."
},
{
"variable": "m",
"dividend": 314,
"divisor": 45,
"remainder": 44,
"description": "Let m be the remainder when y + 300 is divided by 45."
},
{
"variable": "p",
"dividend": 882,
"divisor": 83,
"remainder": 52,
"description": "Let p be the remainder when y + 868 is divided by 83."
},
{
"variable": "g",
"dividend": 904,
"divisor": 72,
"remainder": 40,
"description": "Let g be the remainder when y + 890 is divided by 72."
},
{
"variable": "i",
"dividend": 729,
"divisor": 26,
"remainder": 1,
"description": "Let i be the remainder when y + 715 is divided by 26."
},
{
"variable": "b",
"dividend": 646,
"divisor": 91,
"remainder": 9,
"description": "Let b be the remainder when p - g - m + i + 677 is divided by 91."
}
],
"final_dividend": 848,
"final_remainder": 8,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let p be the remainder when 205 is divided by 26. Let y be the remainder when 702 is divided by 74. Let q be the remainder when y - p + 384 is divided by 31. Let a be the remainder when y - p + 437 is divided by 76. Let m be the remainder when a - q + 74 is divided by 55. Let b be the remainder when m + 835 is divided by 38. Let t be the remainder when b + 843 is divided by 37. Let d be the remainder when t + 616 is divided by 85. Let h be the remainder when d + 454 is divided by 25. Let i be the remainder when d + 976 is divided by 58. What is the remainder when i - h + 758 is divided by 91?
Please reason step by step, and put your final answer within \boxed{}.
|
41
| 67
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2 -> 3, 4 -> 5 -> 6 -> 7 -> 8 -> 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "p",
"dividend": 205,
"divisor": 26,
"remainder": 23,
"description": "Let p be the remainder when 205 is divided by 26."
},
{
"variable": "y",
"dividend": 702,
"divisor": 74,
"remainder": 36,
"description": "Let y be the remainder when 702 is divided by 74."
},
{
"variable": "q",
"dividend": 397,
"divisor": 31,
"remainder": 25,
"description": "Let q be the remainder when y - p + 384 is divided by 31."
},
{
"variable": "a",
"dividend": 450,
"divisor": 76,
"remainder": 70,
"description": "Let a be the remainder when y - p + 437 is divided by 76."
},
{
"variable": "m",
"dividend": 119,
"divisor": 55,
"remainder": 9,
"description": "Let m be the remainder when a - q + 74 is divided by 55."
},
{
"variable": "b",
"dividend": 844,
"divisor": 38,
"remainder": 8,
"description": "Let b be the remainder when m + 835 is divided by 38."
},
{
"variable": "t",
"dividend": 851,
"divisor": 37,
"remainder": 0,
"description": "Let t be the remainder when b + 843 is divided by 37."
},
{
"variable": "d",
"dividend": 616,
"divisor": 85,
"remainder": 21,
"description": "Let d be the remainder when t + 616 is divided by 85."
},
{
"variable": "h",
"dividend": 475,
"divisor": 25,
"remainder": 0,
"description": "Let h be the remainder when d + 454 is divided by 25."
},
{
"variable": "i",
"dividend": 997,
"divisor": 58,
"remainder": 11,
"description": "Let i be the remainder when d + 976 is divided by 58."
}
],
"final_dividend": 769,
"final_remainder": 41,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let z be the remainder when 310 is divided by 29. Let n be the remainder when z + 725 is divided by 97. Let d be the remainder when n + 464 is divided by 48. Let f be the remainder when d + 776 is divided by 22. Let a be the remainder when d + 735 is divided by 44. Let o be the remainder when d + 238 is divided by 99. Let k be the remainder when d + 621 is divided by 23. Let l be the remainder when o + a - k + f + 385 is divided by 46. Let r be the remainder when o - k - f + a + 37 is divided by 47. Let p be the remainder when o + a - k + f + 678 is divided by 95. What is the remainder when r - p - l + 294 is divided by 39?
Please reason step by step, and put your final answer within \boxed{}.
|
7
| 68
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3 -> 4, 5, 6, 7 -> 8, 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "z",
"dividend": 310,
"divisor": 29,
"remainder": 20,
"description": "Let z be the remainder when 310 is divided by 29."
},
{
"variable": "n",
"dividend": 745,
"divisor": 97,
"remainder": 66,
"description": "Let n be the remainder when z + 725 is divided by 97."
},
{
"variable": "d",
"dividend": 530,
"divisor": 48,
"remainder": 2,
"description": "Let d be the remainder when n + 464 is divided by 48."
},
{
"variable": "f",
"dividend": 778,
"divisor": 22,
"remainder": 8,
"description": "Let f be the remainder when d + 776 is divided by 22."
},
{
"variable": "a",
"dividend": 737,
"divisor": 44,
"remainder": 33,
"description": "Let a be the remainder when d + 735 is divided by 44."
},
{
"variable": "o",
"dividend": 240,
"divisor": 99,
"remainder": 42,
"description": "Let o be the remainder when d + 238 is divided by 99."
},
{
"variable": "k",
"dividend": 623,
"divisor": 23,
"remainder": 2,
"description": "Let k be the remainder when d + 621 is divided by 23."
},
{
"variable": "l",
"dividend": 466,
"divisor": 46,
"remainder": 6,
"description": "Let l be the remainder when o + a - k + f + 385 is divided by 46."
},
{
"variable": "r",
"dividend": 102,
"divisor": 47,
"remainder": 8,
"description": "Let r be the remainder when o - k - f + a + 37 is divided by 47."
},
{
"variable": "p",
"dividend": 759,
"divisor": 95,
"remainder": 94,
"description": "Let p be the remainder when o + a - k + f + 678 is divided by 95."
}
],
"final_dividend": 202,
"final_remainder": 7,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let d be the remainder when 779 is divided by 27. Let o be the remainder when d + 413 is divided by 31. Let u be the remainder when o + 734 is divided by 66. Let p be the remainder when o + 479 is divided by 21. Let y be the remainder when o + 214 is divided by 33. Let w be the remainder when o + 565 is divided by 61. Let j be the remainder when o + 804 is divided by 59. Let b be the remainder when j + y - w - u - p + 275 is divided by 63. Let t be the remainder when b + 693 is divided by 55. Let g be the remainder when t + 947 is divided by 97. What is the remainder when g + 509 is divided by 26?
Please reason step by step, and put your final answer within \boxed{}.
|
22
| 69
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3, 4, 5, 6, 7 -> 8 -> 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "d",
"dividend": 779,
"divisor": 27,
"remainder": 23,
"description": "Let d be the remainder when 779 is divided by 27."
},
{
"variable": "o",
"dividend": 436,
"divisor": 31,
"remainder": 2,
"description": "Let o be the remainder when d + 413 is divided by 31."
},
{
"variable": "u",
"dividend": 736,
"divisor": 66,
"remainder": 10,
"description": "Let u be the remainder when o + 734 is divided by 66."
},
{
"variable": "p",
"dividend": 481,
"divisor": 21,
"remainder": 19,
"description": "Let p be the remainder when o + 479 is divided by 21."
},
{
"variable": "y",
"dividend": 216,
"divisor": 33,
"remainder": 18,
"description": "Let y be the remainder when o + 214 is divided by 33."
},
{
"variable": "w",
"dividend": 567,
"divisor": 61,
"remainder": 18,
"description": "Let w be the remainder when o + 565 is divided by 61."
},
{
"variable": "j",
"dividend": 806,
"divisor": 59,
"remainder": 39,
"description": "Let j be the remainder when o + 804 is divided by 59."
},
{
"variable": "b",
"dividend": 285,
"divisor": 63,
"remainder": 33,
"description": "Let b be the remainder when j + y - w - u - p + 275 is divided by 63."
},
{
"variable": "t",
"dividend": 726,
"divisor": 55,
"remainder": 11,
"description": "Let t be the remainder when b + 693 is divided by 55."
},
{
"variable": "g",
"dividend": 958,
"divisor": 97,
"remainder": 85,
"description": "Let g be the remainder when t + 947 is divided by 97."
}
],
"final_dividend": 594,
"final_remainder": 22,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let z be the remainder when 637 is divided by 96. Let f be the remainder when 841 is divided by 83. Let x be the remainder when z - f + 727 is divided by 38. Let b be the remainder when f - z + 1009 is divided by 71. Let m be the remainder when f - z + 1022 is divided by 88. Let w be the remainder when b - m - x + 369 is divided by 31. Let l be the remainder when w + 316 is divided by 74. Let s be the remainder when w + 475 is divided by 92. Let r be the remainder when w + 168 is divided by 40. Let k be the remainder when l - s - r + 438 is divided by 66. What is the remainder when k + 582 is divided by 25?
Please reason step by step, and put your final answer within \boxed{}.
|
9
| 70
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2 -> 3, 4, 5 -> 6 -> 7, 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "z",
"dividend": 637,
"divisor": 96,
"remainder": 61,
"description": "Let z be the remainder when 637 is divided by 96."
},
{
"variable": "f",
"dividend": 841,
"divisor": 83,
"remainder": 11,
"description": "Let f be the remainder when 841 is divided by 83."
},
{
"variable": "x",
"dividend": 777,
"divisor": 38,
"remainder": 17,
"description": "Let x be the remainder when z - f + 727 is divided by 38."
},
{
"variable": "b",
"dividend": 959,
"divisor": 71,
"remainder": 36,
"description": "Let b be the remainder when f - z + 1009 is divided by 71."
},
{
"variable": "m",
"dividend": 972,
"divisor": 88,
"remainder": 4,
"description": "Let m be the remainder when f - z + 1022 is divided by 88."
},
{
"variable": "w",
"dividend": 384,
"divisor": 31,
"remainder": 12,
"description": "Let w be the remainder when b - m - x + 369 is divided by 31."
},
{
"variable": "l",
"dividend": 328,
"divisor": 74,
"remainder": 32,
"description": "Let l be the remainder when w + 316 is divided by 74."
},
{
"variable": "s",
"dividend": 487,
"divisor": 92,
"remainder": 27,
"description": "Let s be the remainder when w + 475 is divided by 92."
},
{
"variable": "r",
"dividend": 180,
"divisor": 40,
"remainder": 20,
"description": "Let r be the remainder when w + 168 is divided by 40."
},
{
"variable": "k",
"dividend": 423,
"divisor": 66,
"remainder": 27,
"description": "Let k be the remainder when l - s - r + 438 is divided by 66."
}
],
"final_dividend": 609,
"final_remainder": 9,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let r be the remainder when 567 is divided by 95. Let q be the remainder when r + 8 is divided by 56. Let j be the remainder when q + 629 is divided by 52. Let z be the remainder when q + 540 is divided by 86. Let u be the remainder when q + 172 is divided by 67. Let h be the remainder when j - u - z + 668 is divided by 94. Let d be the remainder when h + 138 is divided by 99. Let y be the remainder when d + 594 is divided by 31. Let c be the remainder when d + 199 is divided by 62. Let m be the remainder when c - y + 312 is divided by 88. What is the remainder when m + 888 is divided by 68?
Please reason step by step, and put your final answer within \boxed{}.
|
60
| 71
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3, 4, 5 -> 6 -> 7 -> 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "r",
"dividend": 567,
"divisor": 95,
"remainder": 92,
"description": "Let r be the remainder when 567 is divided by 95."
},
{
"variable": "q",
"dividend": 100,
"divisor": 56,
"remainder": 44,
"description": "Let q be the remainder when r + 8 is divided by 56."
},
{
"variable": "j",
"dividend": 673,
"divisor": 52,
"remainder": 49,
"description": "Let j be the remainder when q + 629 is divided by 52."
},
{
"variable": "z",
"dividend": 584,
"divisor": 86,
"remainder": 68,
"description": "Let z be the remainder when q + 540 is divided by 86."
},
{
"variable": "u",
"dividend": 216,
"divisor": 67,
"remainder": 15,
"description": "Let u be the remainder when q + 172 is divided by 67."
},
{
"variable": "h",
"dividend": 634,
"divisor": 94,
"remainder": 70,
"description": "Let h be the remainder when j - u - z + 668 is divided by 94."
},
{
"variable": "d",
"dividend": 208,
"divisor": 99,
"remainder": 10,
"description": "Let d be the remainder when h + 138 is divided by 99."
},
{
"variable": "y",
"dividend": 604,
"divisor": 31,
"remainder": 15,
"description": "Let y be the remainder when d + 594 is divided by 31."
},
{
"variable": "c",
"dividend": 209,
"divisor": 62,
"remainder": 23,
"description": "Let c be the remainder when d + 199 is divided by 62."
},
{
"variable": "m",
"dividend": 320,
"divisor": 88,
"remainder": 56,
"description": "Let m be the remainder when c - y + 312 is divided by 88."
}
],
"final_dividend": 944,
"final_remainder": 60,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let j be the remainder when 643 is divided by 10. Let f be the remainder when j + 663 is divided by 16. Let y be the remainder when j + 591 is divided by 84. Let x be the remainder when y - f + 777 is divided by 32. Let z be the remainder when f - y + 376 is divided by 87. Let u be the remainder when z - x + 214 is divided by 53. Let b be the remainder when u + 787 is divided by 87. Let n be the remainder when u + 934 is divided by 48. Let a be the remainder when u + 718 is divided by 80. Let g be the remainder when n - a + b + 606 is divided by 35. What is the remainder when g + 790 is divided by 79?
Please reason step by step, and put your final answer within \boxed{}.
|
20
| 72
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2, 3 -> 4, 5 -> 6 -> 7, 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "j",
"dividend": 643,
"divisor": 10,
"remainder": 3,
"description": "Let j be the remainder when 643 is divided by 10."
},
{
"variable": "f",
"dividend": 666,
"divisor": 16,
"remainder": 10,
"description": "Let f be the remainder when j + 663 is divided by 16."
},
{
"variable": "y",
"dividend": 594,
"divisor": 84,
"remainder": 6,
"description": "Let y be the remainder when j + 591 is divided by 84."
},
{
"variable": "x",
"dividend": 773,
"divisor": 32,
"remainder": 5,
"description": "Let x be the remainder when y - f + 777 is divided by 32."
},
{
"variable": "z",
"dividend": 380,
"divisor": 87,
"remainder": 32,
"description": "Let z be the remainder when f - y + 376 is divided by 87."
},
{
"variable": "u",
"dividend": 241,
"divisor": 53,
"remainder": 29,
"description": "Let u be the remainder when z - x + 214 is divided by 53."
},
{
"variable": "b",
"dividend": 816,
"divisor": 87,
"remainder": 33,
"description": "Let b be the remainder when u + 787 is divided by 87."
},
{
"variable": "n",
"dividend": 963,
"divisor": 48,
"remainder": 3,
"description": "Let n be the remainder when u + 934 is divided by 48."
},
{
"variable": "a",
"dividend": 747,
"divisor": 80,
"remainder": 27,
"description": "Let a be the remainder when u + 718 is divided by 80."
},
{
"variable": "g",
"dividend": 615,
"divisor": 35,
"remainder": 20,
"description": "Let g be the remainder when n - a + b + 606 is divided by 35."
}
],
"final_dividend": 810,
"final_remainder": 20,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let d be the remainder when 248 is divided by 58. Let l be the remainder when 157 is divided by 95. Let s be the remainder when l - d + 913 is divided by 44. Let h be the remainder when d - l + 979 is divided by 98. Let x be the remainder when d - l + 669 is divided by 23. Let y be the remainder when d - l + 953 is divided by 98. Let z be the remainder when l - d + 261 is divided by 80. Let t be the remainder when d - l + 605 is divided by 38. Let g be the remainder when t - y - x - z - h + s + 347 is divided by 97. Let a be the remainder when g + 368 is divided by 10. What is the remainder when a + 818 is divided by 69?
Please reason step by step, and put your final answer within \boxed{}.
|
67
| 73
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2 -> 3, 4, 5, 6, 7, 8 -> 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "d",
"dividend": 248,
"divisor": 58,
"remainder": 16,
"description": "Let d be the remainder when 248 is divided by 58."
},
{
"variable": "l",
"dividend": 157,
"divisor": 95,
"remainder": 62,
"description": "Let l be the remainder when 157 is divided by 95."
},
{
"variable": "s",
"dividend": 959,
"divisor": 44,
"remainder": 35,
"description": "Let s be the remainder when l - d + 913 is divided by 44."
},
{
"variable": "h",
"dividend": 933,
"divisor": 98,
"remainder": 51,
"description": "Let h be the remainder when d - l + 979 is divided by 98."
},
{
"variable": "x",
"dividend": 623,
"divisor": 23,
"remainder": 2,
"description": "Let x be the remainder when d - l + 669 is divided by 23."
},
{
"variable": "y",
"dividend": 907,
"divisor": 98,
"remainder": 25,
"description": "Let y be the remainder when d - l + 953 is divided by 98."
},
{
"variable": "z",
"dividend": 307,
"divisor": 80,
"remainder": 67,
"description": "Let z be the remainder when l - d + 261 is divided by 80."
},
{
"variable": "t",
"dividend": 559,
"divisor": 38,
"remainder": 27,
"description": "Let t be the remainder when d - l + 605 is divided by 38."
},
{
"variable": "g",
"dividend": 264,
"divisor": 97,
"remainder": 70,
"description": "Let g be the remainder when t - y - x - z - h + s + 347 is divided by 97."
},
{
"variable": "a",
"dividend": 438,
"divisor": 10,
"remainder": 8,
"description": "Let a be the remainder when g + 368 is divided by 10."
}
],
"final_dividend": 826,
"final_remainder": 67,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let z be the remainder when 638 is divided by 50. Let b be the remainder when z + 595 is divided by 33. Let l be the remainder when b + 257 is divided by 74. Let j be the remainder when l + 608 is divided by 79. Let g be the remainder when l + 416 is divided by 21. Let p be the remainder when g - j + 324 is divided by 37. Let r be the remainder when g - j + 557 is divided by 70. Let v be the remainder when g - j + 491 is divided by 92. Let c be the remainder when g - j + 630 is divided by 59. Let t be the remainder when p - v - r + c + 228 is divided by 75. What is the remainder when t + 843 is divided by 31?
Please reason step by step, and put your final answer within \boxed{}.
|
23
| 74
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3 -> 4, 5 -> 6, 7, 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "z",
"dividend": 638,
"divisor": 50,
"remainder": 38,
"description": "Let z be the remainder when 638 is divided by 50."
},
{
"variable": "b",
"dividend": 633,
"divisor": 33,
"remainder": 6,
"description": "Let b be the remainder when z + 595 is divided by 33."
},
{
"variable": "l",
"dividend": 263,
"divisor": 74,
"remainder": 41,
"description": "Let l be the remainder when b + 257 is divided by 74."
},
{
"variable": "j",
"dividend": 649,
"divisor": 79,
"remainder": 17,
"description": "Let j be the remainder when l + 608 is divided by 79."
},
{
"variable": "g",
"dividend": 457,
"divisor": 21,
"remainder": 16,
"description": "Let g be the remainder when l + 416 is divided by 21."
},
{
"variable": "p",
"dividend": 323,
"divisor": 37,
"remainder": 27,
"description": "Let p be the remainder when g - j + 324 is divided by 37."
},
{
"variable": "r",
"dividend": 556,
"divisor": 70,
"remainder": 66,
"description": "Let r be the remainder when g - j + 557 is divided by 70."
},
{
"variable": "v",
"dividend": 490,
"divisor": 92,
"remainder": 30,
"description": "Let v be the remainder when g - j + 491 is divided by 92."
},
{
"variable": "c",
"dividend": 629,
"divisor": 59,
"remainder": 39,
"description": "Let c be the remainder when g - j + 630 is divided by 59."
},
{
"variable": "t",
"dividend": 198,
"divisor": 75,
"remainder": 48,
"description": "Let t be the remainder when p - v - r + c + 228 is divided by 75."
}
],
"final_dividend": 891,
"final_remainder": 23,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let n be the remainder when 257 is divided by 97. Let d be the remainder when n + 771 is divided by 68. Let c be the remainder when d + 171 is divided by 14. Let h be the remainder when c + 275 is divided by 16. Let q be the remainder when h + 162 is divided by 81. Let z be the remainder when h + 354 is divided by 39. Let b be the remainder when z - q + 114 is divided by 59. Let r be the remainder when b + 163 is divided by 96. Let p be the remainder when b + 779 is divided by 92. Let i be the remainder when p - r + 634 is divided by 84. What is the remainder when i + 370 is divided by 23?
Please reason step by step, and put your final answer within \boxed{}.
|
5
| 75
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2 -> 3 -> 4 -> 5, 6 -> 7 -> 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "n",
"dividend": 257,
"divisor": 97,
"remainder": 63,
"description": "Let n be the remainder when 257 is divided by 97."
},
{
"variable": "d",
"dividend": 834,
"divisor": 68,
"remainder": 18,
"description": "Let d be the remainder when n + 771 is divided by 68."
},
{
"variable": "c",
"dividend": 189,
"divisor": 14,
"remainder": 7,
"description": "Let c be the remainder when d + 171 is divided by 14."
},
{
"variable": "h",
"dividend": 282,
"divisor": 16,
"remainder": 10,
"description": "Let h be the remainder when c + 275 is divided by 16."
},
{
"variable": "q",
"dividend": 172,
"divisor": 81,
"remainder": 10,
"description": "Let q be the remainder when h + 162 is divided by 81."
},
{
"variable": "z",
"dividend": 364,
"divisor": 39,
"remainder": 13,
"description": "Let z be the remainder when h + 354 is divided by 39."
},
{
"variable": "b",
"dividend": 117,
"divisor": 59,
"remainder": 58,
"description": "Let b be the remainder when z - q + 114 is divided by 59."
},
{
"variable": "r",
"dividend": 221,
"divisor": 96,
"remainder": 29,
"description": "Let r be the remainder when b + 163 is divided by 96."
},
{
"variable": "p",
"dividend": 837,
"divisor": 92,
"remainder": 9,
"description": "Let p be the remainder when b + 779 is divided by 92."
},
{
"variable": "i",
"dividend": 614,
"divisor": 84,
"remainder": 26,
"description": "Let i be the remainder when p - r + 634 is divided by 84."
}
],
"final_dividend": 396,
"final_remainder": 5,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let a be the remainder when 239 is divided by 38. Let f be the remainder when 915 is divided by 60. Let x be the remainder when f - a + 662 is divided by 47. Let m be the remainder when f - a + 646 is divided by 28. Let r be the remainder when a - f + 320 is divided by 20. Let y be the remainder when a - f + 735 is divided by 92. Let c be the remainder when f - a + 756 is divided by 34. Let s be the remainder when c - y - m - x + r + 860 is divided by 19. Let h be the remainder when r - m - y - x - c + 776 is divided by 22. Let o be the remainder when s - h + 363 is divided by 50. What is the remainder when o + 827 is divided by 38?
Please reason step by step, and put your final answer within \boxed{}.
|
31
| 76
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2 -> 3, 4, 5, 6, 7 -> 8, 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "a",
"dividend": 239,
"divisor": 38,
"remainder": 11,
"description": "Let a be the remainder when 239 is divided by 38."
},
{
"variable": "f",
"dividend": 915,
"divisor": 60,
"remainder": 15,
"description": "Let f be the remainder when 915 is divided by 60."
},
{
"variable": "x",
"dividend": 666,
"divisor": 47,
"remainder": 8,
"description": "Let x be the remainder when f - a + 662 is divided by 47."
},
{
"variable": "m",
"dividend": 650,
"divisor": 28,
"remainder": 6,
"description": "Let m be the remainder when f - a + 646 is divided by 28."
},
{
"variable": "r",
"dividend": 316,
"divisor": 20,
"remainder": 16,
"description": "Let r be the remainder when a - f + 320 is divided by 20."
},
{
"variable": "y",
"dividend": 731,
"divisor": 92,
"remainder": 87,
"description": "Let y be the remainder when a - f + 735 is divided by 92."
},
{
"variable": "c",
"dividend": 760,
"divisor": 34,
"remainder": 12,
"description": "Let c be the remainder when f - a + 756 is divided by 34."
},
{
"variable": "s",
"dividend": 787,
"divisor": 19,
"remainder": 8,
"description": "Let s be the remainder when c - y - m - x + r + 860 is divided by 19."
},
{
"variable": "h",
"dividend": 679,
"divisor": 22,
"remainder": 19,
"description": "Let h be the remainder when r - m - y - x - c + 776 is divided by 22."
},
{
"variable": "o",
"dividend": 352,
"divisor": 50,
"remainder": 2,
"description": "Let o be the remainder when s - h + 363 is divided by 50."
}
],
"final_dividend": 829,
"final_remainder": 31,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let f be the remainder when 598 is divided by 49. Let a be the remainder when 279 is divided by 23. Let o be the remainder when 183 is divided by 87. Let s be the remainder when 651 is divided by 27. Let k be the remainder when a + s - o + f + 130 is divided by 43. Let r be the remainder when o - f - a - s + 244 is divided by 43. Let b be the remainder when s + o + a - f + 258 is divided by 74. Let c be the remainder when s - f + o - a + 338 is divided by 82. Let i be the remainder when a - s - f - o + 584 is divided by 43. Let p be the remainder when a - s - f - o + 493 is divided by 15. What is the remainder when p - i - r - b - k - c + 690 is divided by 85?
Please reason step by step, and put your final answer within \boxed{}.
|
18
| 77
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1, 2, 3, 4 -> 5, 6, 7, 8, 9, 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "f",
"dividend": 598,
"divisor": 49,
"remainder": 10,
"description": "Let f be the remainder when 598 is divided by 49."
},
{
"variable": "a",
"dividend": 279,
"divisor": 23,
"remainder": 3,
"description": "Let a be the remainder when 279 is divided by 23."
},
{
"variable": "o",
"dividend": 183,
"divisor": 87,
"remainder": 9,
"description": "Let o be the remainder when 183 is divided by 87."
},
{
"variable": "s",
"dividend": 651,
"divisor": 27,
"remainder": 3,
"description": "Let s be the remainder when 651 is divided by 27."
},
{
"variable": "k",
"dividend": 137,
"divisor": 43,
"remainder": 8,
"description": "Let k be the remainder when a + s - o + f + 130 is divided by 43."
},
{
"variable": "r",
"dividend": 237,
"divisor": 43,
"remainder": 22,
"description": "Let r be the remainder when o - f - a - s + 244 is divided by 43."
},
{
"variable": "b",
"dividend": 263,
"divisor": 74,
"remainder": 41,
"description": "Let b be the remainder when s + o + a - f + 258 is divided by 74."
},
{
"variable": "c",
"dividend": 337,
"divisor": 82,
"remainder": 9,
"description": "Let c be the remainder when s - f + o - a + 338 is divided by 82."
},
{
"variable": "i",
"dividend": 565,
"divisor": 43,
"remainder": 6,
"description": "Let i be the remainder when a - s - f - o + 584 is divided by 43."
},
{
"variable": "p",
"dividend": 474,
"divisor": 15,
"remainder": 9,
"description": "Let p be the remainder when a - s - f - o + 493 is divided by 15."
}
],
"final_dividend": 613,
"final_remainder": 18,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
Let t be the remainder when 716 is divided by 56. Let n be the remainder when t + 732 is divided by 25. Let s be the remainder when t + 886 is divided by 63. Let u be the remainder when n - s + 751 is divided by 24. Let k be the remainder when u + 945 is divided by 92. Let a be the remainder when k + 316 is divided by 12. Let l be the remainder when k + 654 is divided by 26. Let y be the remainder when a - l + 374 is divided by 27. Let g be the remainder when y + 502 is divided by 76. Let d be the remainder when g + 882 is divided by 94. What is the remainder when d + 186 is divided by 46?
Please reason step by step, and put your final answer within \boxed{}.
|
3
| 78
|
math_datasets_div_remainder_composed
|
{
"type": "div_remainder_composed",
"structure": "1 -> 2, 3 -> 4 -> 5 -> 6, 7 -> 8 -> 9 -> 10 -> final",
"num_compositions": 10,
"sub_equations": [
{
"variable": "t",
"dividend": 716,
"divisor": 56,
"remainder": 44,
"description": "Let t be the remainder when 716 is divided by 56."
},
{
"variable": "n",
"dividend": 776,
"divisor": 25,
"remainder": 1,
"description": "Let n be the remainder when t + 732 is divided by 25."
},
{
"variable": "s",
"dividend": 930,
"divisor": 63,
"remainder": 48,
"description": "Let s be the remainder when t + 886 is divided by 63."
},
{
"variable": "u",
"dividend": 704,
"divisor": 24,
"remainder": 8,
"description": "Let u be the remainder when n - s + 751 is divided by 24."
},
{
"variable": "k",
"dividend": 953,
"divisor": 92,
"remainder": 33,
"description": "Let k be the remainder when u + 945 is divided by 92."
},
{
"variable": "a",
"dividend": 349,
"divisor": 12,
"remainder": 1,
"description": "Let a be the remainder when k + 316 is divided by 12."
},
{
"variable": "l",
"dividend": 687,
"divisor": 26,
"remainder": 11,
"description": "Let l be the remainder when k + 654 is divided by 26."
},
{
"variable": "y",
"dividend": 364,
"divisor": 27,
"remainder": 13,
"description": "Let y be the remainder when a - l + 374 is divided by 27."
},
{
"variable": "g",
"dividend": 515,
"divisor": 76,
"remainder": 59,
"description": "Let g be the remainder when y + 502 is divided by 76."
},
{
"variable": "d",
"dividend": 941,
"divisor": 94,
"remainder": 1,
"description": "Let d be the remainder when g + 882 is divided by 94."
}
],
"final_dividend": 187,
"final_remainder": 3,
"module_name": "div_remainder_composed",
"seed": 42,
"min_dividend": 100,
"max_dividend": 1000,
"min_divisor": 10,
"max_divisor": 100,
"composition_structure": "mixed"
}
|
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