prompt_idx int64 0 16.7k | prompt stringlengths 1.47k 7.34k | response stringlengths 1.46k 138k | source int64 -1 7 | average_correctness float64 0 1 |
|---|---|---|---|---|
0 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | Okay, let's see. I need to solve this problem where they define a special operation ⊗ for all nonzero numbers a and b as a⊗b = a²/b. Then I have to compute [(1⊗2)⊗3] - [1⊗(2⊗3)] and choose the correct answer from the options given. The answer choices are fractions, so the result is probably a fraction. Let me break it ... | 2 | 1 |
1 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | Alright, let's try to figure out the side length of Doug's square window. So, the problem says he uses 8 equal-size panes of glass with a height to width ratio of 5:2. There are borders around and between the panes that are 2 inches wide. The answer choices are from 26 to 34, so it's probably somewhere in that range. L... | 0 | 1 |
2 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | Okay, let me try to figure out this problem. So, we have a polynomial P(x) of degree 3n that satisfies certain conditions at points 0, 1, 2, 3, ..., 3n. Specifically, it's given that P(0) = P(3) = ... = P(3n) = 2, P(1) = P(4) = ... = P(3n-2) = 1, P(2) = P(5) = ... = P(3n-1) = 0, and also P(3n+1) = 730. We need to find ... | 5 | 1 |
3 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | Okay, so I need to find the value of 'a' such that when I apply the function f twice to the square root of 2, I get -sqrt(2). The function is given as f(x) = a x squared minus sqrt(2). Hmm, let me break this down step by step.
First, let's make sure I understand the problem correctly. The function f is a quadratic fun... | 4 | 1 |
4 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | Okay, let's tackle this problem step by step. So, the question is about comparing the total cost of buying an appliance in-store versus through a TV ad, and then figuring out how many cents are saved by choosing the TV advertiser. The answer choices are from 6 to 10 cents, so the difference can't be too large. Let me b... | 0 | 1 |
5 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | Okay, let's try to tackle this geometry problem step by step. First, I need to visualize the setup. There are points A, B, C, D, E, and F lying on the line AF in that order, dividing it into five segments each of length 1. So, the total length from A to F is 5 units. Let me sketch this mentally: A to B is 1 unit, B to ... | 5 | 1 |
6 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | Okay, let's see. The problem is about Judy's hits during the softball season. She had a total of 35 hits. Among those, 1 was a home run, 1 was a triple, and 5 were doubles. The rest were singles. We need to find out what percent of her hits were singles. The options are given from A to E.
First, I need to recall how t... | 2 | 1 |
7 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | Okay, let's tackle this problem step by step. The question is about rotating the graph of y = log₁₀x 90 degrees counter-clockwise about the origin and finding the equation of the new graph G'. The options are given, and we need to figure out which one is correct.
First, I need to recall how rotation affects a graph. R... | 2 | 1 |
8 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | Okay, let's try to figure out this problem step by step. So, Jose, Thuy, and Kareem each start with the number 10 and perform different operations. We need to see who ends up with the largest final answer. The options are among them, so let's break down each person's calculations one by one.
First, let's take Jose. Th... | 4 | 1 |
9 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | Alright, let's tackle this problem step by step. So, we have a set of consecutive positive integers starting from 1, and one number is erased. The average of the remaining numbers is \(35\frac{7}{17}\). We need to find out which number was erased. The options are from 6 to 9, or cannot be determined. Hmm, okay.
First,... | 0 | 1 |
10 | <|im_start|>system
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ite... | Okay, let me try to figure out this problem. So, we have a rectangular yard with two flower beds that are congruent isosceles right triangles. The rest of the yard is a trapezoid with parallel sides of 15 and 25 meters. We need to find the fraction of the yard occupied by the flower beds. Hmm, okay.
First, let me visu... | 5 | 1 |
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