prompt_idx int64 0 16.7k | prompt stringlengths 1.47k 7.34k | response stringlengths 861 173k | 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... | Alright, let's tackle this problem step by step. So, we have this operation defined as a⊗b = a²/b, and we need to find the value of [(1⊗2)⊗3] - [1⊗(2⊗3)]. The answer choices are given, so that might help later to check if our calculations are on the right track. Let me start by understanding the operation first.
First... | 0 | 0.375 |
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... | Alright, let's tackle this problem step by step. It's about a cubic polynomial \( P(x) \) of degree \( 3n \) that satisfies certain conditions at points 0, 1, 2, 3, ..., up to \( 3n \), and then another condition at \( x = 3n+1 \). We need to find the value of \( n \) given that \( P(3n+1) = 730 \).
First, let me pars... | 0 | 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... | Alright, let's tackle this problem step by step. So, we have the function f(x) = a x² - √2, and we need to find the positive constant a such that f(f(√2)) = -√2. The answer choices are given, so eventually, we have to match our solution with one of those. Let me start by understanding what the problem is asking.
First... | 0 | 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... | Alright, let's 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 C is... | 0 | 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 tackle this problem step by step. So, Judy had 35 hits during the softball season. Among those, she had 1 home run, 1 triple, and 5 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 to calculate percent... | 0 | 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... | Alright, let's tackle this problem step by step. So, we have the graph of y = log₁₀x, and it's being rotated 90 degrees counter-clockwise about the origin to form a new graph G'. We need to figure out which of the given options is the equation for G'. Hmm, okay. Let me start by recalling how rotations affect points and... | 0 | 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... | Alright, let's tackle this problem step by step. So, we have three people—Jose, Thuy, and Kareem—each starting with the number 10. They each perform different operations, and we need to figure out who ends up with the largest final answer. The answer choices are given, so we have to calculate each person's result and c... | 0 | 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 |
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