prompt_idx int64 0 16.7k | prompt stringlengths 1.47k 7.34k | response stringlengths 861 200k | 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, so I need to solve this problem where they define a special operation called ⊗. The operation is defined 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 given options. Let me start by understanding the operation step by step.
Firs... | 4 | 0.5 |
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... | Okay, so Doug is building this square window with 8 equal-sized panes of glass. Each pane has a height to width ratio of 5:2. There are borders around and between the panes that are 2 inches wide. The question is asking for the side length of the square window in inches. The answer choices are from 26 to 34, so it's a ... | 7 | 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, so I need to find the value of n given this polynomial P(x) of degree 3n that satisfies various conditions at points 0, 1, 2, 3, ..., 3n, and also P(3n+1) = 730. Let me try to break this down step by step.
First, let me understand the problem. The polynomial P(x) has degree 3n. That's important because a polynom... | 4 | 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, let me try to solve this problem step by step. The function is given as f(x) = a x² - √2, and we need to find the positive value of a such that f(f(√2)) = -√2. The answer choices are given, so maybe after working through the problem, I can check which one matches.
First, let's break down what f(f(√2)) means. It ... | 3 | 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 see. The problem 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 break it down step by step.
First,... | 3 | 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, so I need to solve this geometry problem. Let me read it again carefully.
Points A, B, C, D, E, and F lie on AF in that order, dividing it into five segments each of length 1. So that means AF is divided into five equal parts, each 1 unit long. So the distance from A to F is 5 units. The points are A, B, C, D, E... | 4 | 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... | 1 | 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 from (A) to (E), and I need to figure out which one is correct.
First, I need to recall how rotation aff... | 6 | 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 tackle this problem step by step. So, we have 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 after calculating each person's result, we can compare them.
F... | 2 | 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... | Okay, let me try to figure out this problem. 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 and 7/17. We need to find out which number was erased. The options are from 6 to 9, or cannot be determined. Hmm, let's break this down st... | 3 | 0.25 |
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