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67
"<|im_start|>system\nPlease reason step by step. Think through the problem in depth before answering(...TRUNCATED)
["<think>\nOkay, so I need to solve this problem where the product of logarithms with bases a, a+1, (...TRUNCATED)
[ 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1 ]
[ 1, 1, 1, 1, 1, 1, 1, 1, 24, 24, 24, 24, 24, 24, 24, 24, 73, 73, 73, 73, 73, 73, 73, 73 ]
1,508
"<|im_start|>system\nPlease reason step by step. Think through the problem in depth before answering(...TRUNCATED)
["<think>\nOkay, so I need to find the probability that a randomly chosen integer from 1 to 100 is a(...TRUNCATED)
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
[ 1, 1, 1, 1, 1, 1, 1, 1, 49, 49, 49, 49, 49, 49, 49, 49, 72, 72, 72, 72, 72, 72, 72, 72 ]
3,587
"<|im_start|>system\nPlease reason step by step. Think through the problem in depth before answering(...TRUNCATED)
["<think>\nOkay, so I have this problem here: I need to find all values of k for which the positive (...TRUNCATED)
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
[ 1, 1, 1, 1, 1, 1, 1, 1, 32, 32, 32, 32, 32, 32, 32, 32 ]
967
"<|im_start|>system\nPlease reason step by step. Think through the problem in depth before answering(...TRUNCATED)
["<think>\nOkay, so I have this problem here about feathers and gold, and I need to find the cost of(...TRUNCATED)
[ 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1 ]
[ 1, 1, 1, 1, 1, 1, 1, 1, 51, 51, 51, 51, 51, 51, 51, 51, 85, 85, 85, 85, 85, 85, 85, 85 ]
6,912
"<|im_start|>system\nPlease reason step by step. Think through the problem in depth before answering(...TRUNCATED)
["<think>\nOkay, so I need to find the average of all distinct possible values of t for the polynomi(...TRUNCATED)
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
[ 1, 1, 1, 1, 1, 1, 1, 1, 45, 45, 45, 45, 45, 45, 45, 45, 90, 90, 90, 90, 90, 90, 90, 90 ]
2,726
"<|im_start|>system\nPlease reason step by step. Think through the problem in depth before answering(...TRUNCATED)
["<think>\nOkay, so I need to find the circumference of a circle that's inscribed in a square with a(...TRUNCATED)
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
[ 1, 1, 1, 1, 1, 1, 1, 1, 22, 22, 22, 22, 22, 22, 22, 22, 76, 76, 76, 76, 76, 76, 76, 76 ]
2,987
"<|im_start|>system\nPlease reason step by step. Think through the problem in depth before answering(...TRUNCATED)
["<think>\nOkay, so I have this equation here: \\(\\log_{10x^2} 10 + \\log_{100x^3} 10 = -2\\). I ne(...TRUNCATED)
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
[ 1, 1, 1, 1, 1, 1, 1, 1, 26, 26, 26, 26, 26, 26, 26, 26 ]
595
"<|im_start|>system\nPlease reason step by step. Think through the problem in depth before answering(...TRUNCATED)
["<think>\nOkay, let me try to figure out how to simplify this expression: \\(\\frac{\\tan 30^\\circ(...TRUNCATED)
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
[ 1, 1, 1, 1, 1, 1, 1, 1, 50, 50, 50, 50, 50, 50, 50, 50 ]
752
"<|im_start|>system\nPlease reason step by step. Think through the problem in depth before answering(...TRUNCATED)
["<think>\nOkay, let me see. So I have this problem here about a right triangle EAD with the right a(...TRUNCATED)
[ 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0 ]
[ 1, 1, 1, 1, 1, 1, 1, 1, 56, 56, 56, 56, 56, 56, 56, 56 ]
7,351
"<|im_start|>system\nPlease reason step by step. Think through the problem in depth before answering(...TRUNCATED)
["<think>\nOkay, so I have this problem here: \"The greatest common divisor of two positive integers(...TRUNCATED)
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
[ 1, 1, 1, 1, 1, 1, 1, 1, 35, 35, 35, 35, 35, 35, 35, 35, 73, 73, 73, 73, 73, 73, 73, 73 ]
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