prompt_idx int64 0 16.7k | prompt stringclasses 998
values | response stringlengths 1.7k 168k | source int64 -1 7 | weight float64 0 8 |
|---|---|---|---|---|
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 there's a custom operation defined for all nonzero numbers. The operation is called "β" and it's defined by aβb = aΒ² / b. The question is asking for the value of [(1β2)β3] - [1β(2β3)]. The answer choices are given from A to E. Alright, let me break this down step by s... | 6 | 5.336447 |
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 called "β" defined for all nonzero numbers by aβb = aΒ²/b. The question is asking us to compute [(1β2)β3] - [1β(2β3)] and then choose the correct option from A to E. Hmm, okay. Let me break this down.
First, I need to remember how the operation... | 0 | 1.094282 |
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 me try to solve this problem step by step. The problem is about an operation called "β" defined for all nonzero numbers by aβb = aΒ² / b. We need to compute [(1β2)β3] - [1β(2β3)] and choose the correct answer from the options given.
First, let me make sure I understand the operation. The operation β takes tw... | 3 | 0.412764 |
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 an operation β for all nonzero numbers. The operation is given by aβb = aΒ²βb. Then I have to compute [(1β2)β3] - [1β(2β3)] and choose the correct answer from the options provided. Alright, let's break this down step by step.
First, I should probably comp... | 7 | 0.254007 |
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 tackle this problem step by step. The question is about an operation defined by \( a \otimes b = \frac{a^2}{b} \). We need to compute \( [(1 \otimes 2) \otimes 3] - [1 \otimes (2 \otimes 3)] \) and choose the correct answer from the options given.
First, I need to make sure I understand how the operation ... | 5 | 0.249054 |
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 figure out this problem where they define a new operation called β. The operation is for all nonzero numbers, and it's defined as aβb = aΒ² / b. Then I have to compute [(1β2)β3] - [1β(2β3)] and see which of the given options it matches. Let me start by breaking it down step by step.
First, let me rec... | 1 | 0.227237 |
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. The problem is about this operation called "β" defined for all nonzero numbers. The definition is aβb = aΒ² / b. I need to compute [(1β2)β3] - [1β(2β3)] and choose the correct answer from the options given. Alright, let me break this down step by step.
First, I need to understand how the operation work... | 2 | 0.218879 |
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 "β" between two numbers. The operation is given by aβb = aΒ² / b. Then they want me to compute [(1β2)β3] minus [1β(2β3)]. The answer choices are from A to E, with fractions and zero. Let me take it step by step.
First, let me make sure I... | 4 | 0.207332 |
16 | <|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, Alicia has two containers. The first one is 5/6 full of water, and the second is empty. She pours all the water from the first container into the second one, and then the second container becomes 3/4 full. We need to find the ratio of the first container's volume to the s... | 1 | 6.107329 |
16 | <|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, Alicia has two containers. The first one is 5/6 full of water, and the second one is empty. She pours all the water from the first container into the second one, and then the second container is 3/4 full. The question is asking for the ratio of the volume of the first co... | 3 | 0.900804 |
16 | <|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 Alicia having two containers. The first one is 5/6 full of water, and the second is empty. She pours all the water from the first into the second, and then the second container is 3/4 full. We need to find the ratio of the volume of the first container to the volume of the second c... | 6 | 0.811296 |
16 | <|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, Alicia has two containers. The first one is 5/6 full of water, and the second one is empty. She pours all the water from the first container into the second one. After that, the second container is 3/4 full. We need to find the ratio of the first container's volume to t... | 5 | 0.135281 |
16 | <|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 says that Alicia had two containers. The first one was 5/6 full of water, and the second was empty. She poured all the water from the first container into the second one, and then the second container was 3/4 full. We need to find the ratio of the first container's volume to the second cont... | 2 | 0.04097 |
16 | <|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 solve this problem step by step. So, Alicia has two containers. The first one is 5/6 full of water, and the second one is empty. She pours all the water from the first container into the second one, and then the second container becomes 3/4 full. We need to find the ratio of the volume of the first c... | 4 | 0.0039 |
16 | <|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. Alicia has two containers. The first one is 5/6 full of water, and the second one is empty. She pours all the water from the first into the second, and then the second container is 3/4 full. The question is asking for the ratio of the volume of the first container to the volume of the second container.... | 7 | 0.000391 |
16 | <|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, Alicia has two containers. The first one is 5/6 full of water, and the second one is empty. Then she pours all the water from the first container into the second one, and after doing that, the second container is 3/4 full. We need to find the ratio of the volume of the ... | 0 | 0.000029 |
33 | <|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 a multiplication problem where the numbers involved are ABA (a three-digit number) multiplied by CD (a two-digit number), and the product is CDCD (a four-digit number). All the letters A, B, C, D represent different digits, and we need to find A + B. The options... | 5 | 1.911447 |
33 | <|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, we have a multiplication problem where A, B, C, D are different digits. The problem is set up like this:
```
A B A
Γ C D
-------
C D C D
```
And we need to find A + B. The answer choices are 1, 2, 3, 4, or 9. Alright, let's start by understanding what this multiplica... | 1 | 1.360869 |
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