prompt_idx int64 0 16.7k | prompt stringlengths 1.47k 7.34k | response stringlengths 1.28k 178k | source int64 -1 7 | average_correctness float64 0 1 |
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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 compute [(1⊗2)⊗3] - [1⊗(2⊗3)]. The answer choices are given, so hopefully, after working through it, one of those will pop out. Let me start by understanding the operation first.
First, the operation ⊗ i... | 0 | 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 tackle this problem step by step. So, Doug is building a square window with 8 equal-size panes of glass. Each pane has a height to width ratio of 5:2, and there are borders around and between the panes that are 2 inches wide everywhere. We need to find the side length of the square window. The answer cho... | 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 polynomial problem. Hmm, so we have a polynomial P(x) of degree 3n. The conditions given are that P(0) = P(3) = ... = P(3n) = 2, P(1) = P(4) = ... = P(3n-2) = 1, and P(2) = P(5) = ... = P(3n-1) = 0. Also, P(3n+1) = 730. We need to find n.
First, let's parse the problem. The polynomial is of ... | 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 a function f defined as f(x) = a x² - √2, where a is some positive constant. The question says that f(f(√2)) equals -√2, and we need to find the value of a from the given options. Hmm, okay. Let me write down what I know and see how to approach this.
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... | Alright, let's tackle this problem step by step. So, the question is about figuring out how many cents are saved by buying the appliance from the television advertiser compared to the in-store price. The options are from A to E, with the answers in cents, so I need to make sure my calculations are precise enough to get... | 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 me try to work through this geometry problem. Hmm, so we have points A, B, C, D, E, F on line AF, each dividing it into five equal segments of length 1. So AF is a line segment divided into five parts, each 1 unit long. Then point G is not on AF, which means it's somewhere off the line. Points H is on GD, and... | 3 | 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. Judy had a total of 35 hits during the softball season. Now, among those hits, she had some home runs, triples, doubles, and singles. The problem says she had 1 home run, 1 triple, and 5 doubles. The rest were singles. We need to find out what percentage of her hits were singles. The options are given ... | 6 | 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, so I need to figure out the equation of the graph G' which is the graph of y = log₁₀x rotated 90 degrees counter-clockwise about the origin. The options are given, and I need to pick the correct one. Let me start by recalling how rotations affect functions.
First, rotating a graph 90 degrees counter-clockwise ar... | 4 | 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. So, Jose, Thuy, and Kareem all start with the number 10. They each do different operations, and we need to see who gets the largest final answer. The options are A through E, with A being Jose, B Thuy, C Kareem, D Jose and Thuy, E Thuy and Kareem. Hmm. Let me break down each ... | 1 | 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, so the problem says there's a set of consecutive positive integers starting from 1. One number is erased, and the average of the remaining numbers is 35 and 7/17. We need to figure out which number was erased. The options are 6, 7, 8, 9, or it's undetermined. Hmm, let's think through this step by step.
First, le... | 1 | 1 |
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