row_index int64 | prompt_id string | messages list | question string | data_source string | ground_truth string | extra_info dict | sample_index int64 | response string | finish_reason string | stop_reason string | response_token_ids list | response_token_count int64 | cumulative_logprob float64 | token_logprobs list | generation dict | reward int64 | group_success_rate float64 | parsed_ground_truth string | parsed_prediction string | answer_extraction string | verifier_error string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 7 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n33. How many six-digit numbers are there in which all digits are odd?\n\nRemember to put your answer on its own line a... | 33. How many six-digit numbers are there in which all digits are odd? | math_dapo | 15625 | {
"index": 7,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 2,
"DeepSeek-R1-Distill-Qwen-7B": 1
},
"original_data_source": "train-math-numinamath1.5_olympiads",
"prompt_style": "dapo_original"
} | 0 | We are asked to find how many **six-digit numbers** exist in which **all digits are odd**.
---
### Step 1: Understand the problem
A **six-digit number** must be between **100,000** and **999,999**.
Each digit in the number must be one of the **odd digits**: **1, 3, 5, 7, 9**.
So, there are **5 choices** for each d... | stop | null | [
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0 | 7 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n33. How many six-digit numbers are there in which all digits are odd?\n\nRemember to put your answer on its own line a... | 33. How many six-digit numbers are there in which all digits are odd? | math_dapo | 15625 | {
"index": 7,
"model_difficulty": {
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"DeepSeek-R1-Distill-Qwen-32B": 2,
"DeepSeek-R1-Distill-Qwen-7B": 1
},
"original_data_source": "train-math-numinamath1.5_olympiads",
"prompt_style": "dapo_original"
} | 1 | To determine how many six-digit numbers have all odd digits, we need to analyze the structure of a six-digit number and the possible values for each digit.
---
### Step 1: Understanding the constraints
A **six-digit number** must be between **100,000** and **999,999**. Therefore, the first digit (the hundred thousan... | stop | null | [
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0 | 7 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n33. How many six-digit numbers are there in which all digits are odd?\n\nRemember to put your answer on its own line a... | 33. How many six-digit numbers are there in which all digits are odd? | math_dapo | 15625 | {
"index": 7,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 2,
"DeepSeek-R1-Distill-Qwen-7B": 1
},
"original_data_source": "train-math-numinamath1.5_olympiads",
"prompt_style": "dapo_original"
} | 2 | We are asked to find how many **six-digit numbers** exist in which **all digits are odd**.
---
### Step 1: Understand the range of six-digit numbers
A **six-digit number** is any number from **100000 to 999999**.
So, the total number of six-digit numbers is:
$$
999999 - 100000 + 1 = 900000
$$
But we're not lookin... | stop | null | [
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0 | 7 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n33. How many six-digit numbers are there in which all digits are odd?\n\nRemember to put your answer on its own line a... | 33. How many six-digit numbers are there in which all digits are odd? | math_dapo | 15625 | {
"index": 7,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 2,
"DeepSeek-R1-Distill-Qwen-7B": 1
},
"original_data_source": "train-math-numinamath1.5_olympiads",
"prompt_style": "dapo_original"
} | 3 | To find how many six-digit numbers have all digits odd, we need to consider the following:
- A six-digit number ranges from **100000 to 999999**.
- The digits that are **odd** are: **1, 3, 5, 7, 9**. So there are **5 choices** for each digit.
- However, the **first digit** (the hundred thousands place) **cannot be 0**... | stop | null | [
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0 | 7 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n33. How many six-digit numbers are there in which all digits are odd?\n\nRemember to put your answer on its own line a... | 33. How many six-digit numbers are there in which all digits are odd? | math_dapo | 15625 | {
"index": 7,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 2,
"DeepSeek-R1-Distill-Qwen-7B": 1
},
"original_data_source": "train-math-numinamath1.5_olympiads",
"prompt_style": "dapo_original"
} | 4 | To solve the problem of how many six-digit numbers exist in which **all digits are odd**, let's go step by step.
---
### Step 1: Understand the constraints
- A **six-digit number** means the number must be between **100,000 and 999,999**.
- All **digits must be odd**: the odd digits are **1, 3, 5, 7, 9**.
- That giv... | stop | null | [
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0 | 7 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n33. How many six-digit numbers are there in which all digits are odd?\n\nRemember to put your answer on its own line a... | 33. How many six-digit numbers are there in which all digits are odd? | math_dapo | 15625 | {
"index": 7,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 2,
"DeepSeek-R1-Distill-Qwen-7B": 1
},
"original_data_source": "train-math-numinamath1.5_olympiads",
"prompt_style": "dapo_original"
} | 5 | We are asked to find how many **six-digit numbers** exist in which **all digits are odd**.
---
### Step 1: Understand the structure of a six-digit number
A six-digit number is any number from **100,000 to 999,999**. So, the first digit (the hundred thousands place) **cannot be zero**.
We are looking for numbers whe... | stop | null | [
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0 | 7 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n33. How many six-digit numbers are there in which all digits are odd?\n\nRemember to put your answer on its own line a... | 33. How many six-digit numbers are there in which all digits are odd? | math_dapo | 15625 | {
"index": 7,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 2,
"DeepSeek-R1-Distill-Qwen-7B": 1
},
"original_data_source": "train-math-numinamath1.5_olympiads",
"prompt_style": "dapo_original"
} | 6 | To find how many six-digit numbers have all **odd digits**, let's break the problem down step by step.
---
### Step 1: Understand the range of six-digit numbers
A **six-digit number** ranges from:
- **100000** (smallest six-digit number)
- **999999** (largest six-digit number)
So, there are $999999 - 100000 + 1 = ... | stop | null | [
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0 | 7 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n33. How many six-digit numbers are there in which all digits are odd?\n\nRemember to put your answer on its own line a... | 33. How many six-digit numbers are there in which all digits are odd? | math_dapo | 15625 | {
"index": 7,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 2,
"DeepSeek-R1-Distill-Qwen-7B": 1
},
"original_data_source": "train-math-numinamath1.5_olympiads",
"prompt_style": "dapo_original"
} | 7 | To determine how many six-digit numbers have **all odd digits**, let's analyze the problem step by step.
---
### Step 1: Understand the range of six-digit numbers
A **six-digit number** ranges from **100000** to **999999**.
So, we are looking for all six-digit numbers where **each digit is odd**.
---
### Step 2: ... | stop | null | [
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1 | 8 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the value of the least positive base ten number which requires six digits for its binary representation?\n\nRe... | What is the value of the least positive base ten number which requires six digits for its binary representation? | math_dapo | 32 | {
"index": 8,
"model_difficulty": {
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"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 0 | We are asked to find the **least positive base ten number** that requires **six digits** in its **binary representation**.
---
### Step 1: Understand binary digit requirements
A number that requires **6 binary digits** must be in the range that begins with the **smallest 6-digit binary number**, which is:
$$
100000_... | stop | null | [
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1 | 8 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the value of the least positive base ten number which requires six digits for its binary representation?\n\nRe... | What is the value of the least positive base ten number which requires six digits for its binary representation? | math_dapo | 32 | {
"index": 8,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 1 | To find the **least positive base ten number** that requires **six digits in its binary representation**, we need to determine the **smallest number** that has **six binary digits**.
---
### Step 1: Understand binary digit lengths
A binary number with $ n $ digits can represent values from:
$$
2^{n-1} \text{ to } 2^... | stop | null | [
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1 | 8 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the value of the least positive base ten number which requires six digits for its binary representation?\n\nRe... | What is the value of the least positive base ten number which requires six digits for its binary representation? | math_dapo | 32 | {
"index": 8,
"model_difficulty": {
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"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 2 | We are looking for the **least positive base ten number** that requires **six digits in its binary representation**.
### Step 1: Understand the binary digit requirement
A number in **binary** requires **6 digits** if it is **between $2^5$ and $2^6 - 1$** (inclusive), because:
- $2^5 = 32$ is the smallest 6-digit bin... | stop | null | [
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1 | 8 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the value of the least positive base ten number which requires six digits for its binary representation?\n\nRe... | What is the value of the least positive base ten number which requires six digits for its binary representation? | math_dapo | 32 | {
"index": 8,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 3 | We are asked to find the **least positive base ten number** that requires **six digits in binary representation**.
---
### Step 1: Understand binary digit length
A number that requires **six binary digits** must be in the range:
$$
2^5 \leq n < 2^6
$$
This is because:
- A 1-bit binary number can represent values ... | stop | null | [
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1 | 8 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the value of the least positive base ten number which requires six digits for its binary representation?\n\nRe... | What is the value of the least positive base ten number which requires six digits for its binary representation? | math_dapo | 32 | {
"index": 8,
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"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 4 | To solve this, we need to determine the **smallest positive number** that requires **6 digits** in its **binary representation**.
---
### Step 1: Understand binary number lengths
The number of digits in the binary representation of a number is determined by the largest power of 2 that is less than or equal to that n... | stop | null | [
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} | 1 | 1 | 32 | 32 | answer | null |
1 | 8 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the value of the least positive base ten number which requires six digits for its binary representation?\n\nRe... | What is the value of the least positive base ten number which requires six digits for its binary representation? | math_dapo | 32 | {
"index": 8,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 5 | We are asked to find the **least positive base ten number** that requires **six digits in its binary representation**.
---
### Step 1: Understand binary digit lengths
A number that requires **6 binary digits** must be in the range:
$$
2^5 \leq N < 2^6
$$
Because:
- A 1-bit binary number is between $ 2^0 = 1 $ and ... | stop | null | [
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1 | 8 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the value of the least positive base ten number which requires six digits for its binary representation?\n\nRe... | What is the value of the least positive base ten number which requires six digits for its binary representation? | math_dapo | 32 | {
"index": 8,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 6 | We are asked to find the **least positive base ten number** that requires **six digits in its binary representation**.
---
### Step 1: Understand binary digit length
A number that requires **n digits in binary** must satisfy:
$$
2^{n-1} \leq \text{number} < 2^n
$$
This is because:
- The smallest n-digit binary num... | stop | null | [
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1 | 8 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the value of the least positive base ten number which requires six digits for its binary representation?\n\nRe... | What is the value of the least positive base ten number which requires six digits for its binary representation? | math_dapo | 32 | {
"index": 8,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 7 | We are asked to find the **least positive base ten number** that requires **six digits** in its **binary representation**.
---
### Step 1: Understand the binary digit requirement
A number that requires **6 binary digits** must be **greater than or equal to $2^5 = 32$** and **less than $2^6 = 64$**.
This is because:... | stop | null | [
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2 | 24 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n7.109. $5^{2 x-1}+2^{2 x}-5^{2 x}+2^{2 x+2}=0$.\n\nRemember to put your answer on its own line after \"Answer:\".",
... | 7.109. $5^{2 x-1}+2^{2 x}-5^{2 x}+2^{2 x+2}=0$. | math_dapo | 1 | {
"index": 24,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 1,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-numinamath1.5_olympiads",
"prompt_style": "dapo_original"
} | 0 | We are given the equation:
$$
5^{2x - 1} + 2^{2x} - 5^{2x} + 2^{2x + 2} = 0
$$
---
### Step 1: Simplify the terms
Group like terms:
$$
(5^{2x - 1} - 5^{2x}) + (2^{2x} + 2^{2x + 2}) = 0
$$
---
### Step 2: Simplify each group
**First group:**
$$
5^{2x - 1} - 5^{2x} = 5^{2x - 1} - 5 \cdot 5^{2x - 1} = (1 - 5) \cdo... | stop | null | [
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2 | 24 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n7.109. $5^{2 x-1}+2^{2 x}-5^{2 x}+2^{2 x+2}=0$.\n\nRemember to put your answer on its own line after \"Answer:\".",
... | 7.109. $5^{2 x-1}+2^{2 x}-5^{2 x}+2^{2 x+2}=0$. | math_dapo | 1 | {
"index": 24,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 1,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-numinamath1.5_olympiads",
"prompt_style": "dapo_original"
} | 1 | We are given the equation:
$$
5^{2x-1} + 2^{2x} - 5^{2x} + 2^{2x+2} = 0
$$
### Step 1: Simplify the terms
Let’s simplify each term:
- $5^{2x - 1} = \frac{5^{2x}}{5}$
- $2^{2x+2} = 2^{2x} \cdot 2^2 = 4 \cdot 2^{2x}$
So the equation becomes:
$$
\frac{5^{2x}}{5} + 2^{2x} - 5^{2x} + 4 \cdot 2^{2x} = 0
$$
### Step 2:... | stop | null | [
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2 | 24 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n7.109. $5^{2 x-1}+2^{2 x}-5^{2 x}+2^{2 x+2}=0$.\n\nRemember to put your answer on its own line after \"Answer:\".",
... | 7.109. $5^{2 x-1}+2^{2 x}-5^{2 x}+2^{2 x+2}=0$. | math_dapo | 1 | {
"index": 24,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 1,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-numinamath1.5_olympiads",
"prompt_style": "dapo_original"
} | 2 | We are given the equation:
$$
5^{2x - 1} + 2^{2x} - 5^{2x} + 2^{2x + 2} = 0
$$
### Step 1: Simplify the terms
Let’s rewrite each term using exponent rules.
Recall:
- $5^{2x - 1} = \frac{5^{2x}}{5}$
- $2^{2x + 2} = 2^{2x} \cdot 2^2 = 4 \cdot 2^{2x}$
Now substitute these into the original equation:
$$
\frac{5^{2x}}{... | stop | null | [
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2 | 24 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n7.109. $5^{2 x-1}+2^{2 x}-5^{2 x}+2^{2 x+2}=0$.\n\nRemember to put your answer on its own line after \"Answer:\".",
... | 7.109. $5^{2 x-1}+2^{2 x}-5^{2 x}+2^{2 x+2}=0$. | math_dapo | 1 | {
"index": 24,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 1,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-numinamath1.5_olympiads",
"prompt_style": "dapo_original"
} | 3 | We are given the equation:
$$
5^{2x - 1} + 2^{2x} - 5^{2x} + 2^{2x + 2} = 0
$$
---
### Step 1: Simplify the terms
Group and simplify like terms:
- $5^{2x - 1} - 5^{2x}$
- $2^{2x} + 2^{2x + 2}$
Let’s simplify each part:
---
### Step 2: Simplify $5^{2x - 1} - 5^{2x}$
We can factor out $5^{2x}$:
$$
5^{2x - 1} = ... | stop | null | [
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2 | 24 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n7.109. $5^{2 x-1}+2^{2 x}-5^{2 x}+2^{2 x+2}=0$.\n\nRemember to put your answer on its own line after \"Answer:\".",
... | 7.109. $5^{2 x-1}+2^{2 x}-5^{2 x}+2^{2 x+2}=0$. | math_dapo | 1 | {
"index": 24,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 1,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-numinamath1.5_olympiads",
"prompt_style": "dapo_original"
} | 4 | We are given the equation:
$$
5^{2x - 1} + 2^{2x} - 5^{2x} + 2^{2x + 2} = 0
$$
---
### Step 1: Simplify the terms
We will simplify each term individually.
#### Term 1: $5^{2x - 1}$
$$
5^{2x - 1} = \frac{5^{2x}}{5}
$$
#### Term 2: $2^{2x}$ (already simple)
#### Term 3: $-5^{2x}$ (already simple)
#### Term 4: $2... | stop | null | [
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2 | 24 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n7.109. $5^{2 x-1}+2^{2 x}-5^{2 x}+2^{2 x+2}=0$.\n\nRemember to put your answer on its own line after \"Answer:\".",
... | 7.109. $5^{2 x-1}+2^{2 x}-5^{2 x}+2^{2 x+2}=0$. | math_dapo | 1 | {
"index": 24,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 1,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-numinamath1.5_olympiads",
"prompt_style": "dapo_original"
} | 5 | We are given the equation:
$$
5^{2x-1} + 2^{2x} - 5^{2x} + 2^{2x+2} = 0
$$
### Step 1: Simplify the terms
Group like terms and simplify:
$$
5^{2x-1} - 5^{2x} + 2^{2x} + 2^{2x+2} = 0
$$
Now simplify each exponential term.
#### Simplify $5^{2x-1}$:
$$
5^{2x-1} = \frac{1}{5} \cdot 5^{2x}
$$
#### Simplify $2^{2x+2}$:... | stop | null | [
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2 | 24 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n7.109. $5^{2 x-1}+2^{2 x}-5^{2 x}+2^{2 x+2}=0$.\n\nRemember to put your answer on its own line after \"Answer:\".",
... | 7.109. $5^{2 x-1}+2^{2 x}-5^{2 x}+2^{2 x+2}=0$. | math_dapo | 1 | {
"index": 24,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 1,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-numinamath1.5_olympiads",
"prompt_style": "dapo_original"
} | 6 | We are given the equation:
$$
5^{2x - 1} + 2^{2x} - 5^{2x} + 2^{2x + 2} = 0
$$
---
### **Step 1: Group terms by base**
Group the terms based on the base (5 and 2):
$$
5^{2x - 1} - 5^{2x} + 2^{2x} + 2^{2x + 2} = 0
$$
---
### **Step 2: Simplify each group**
#### **Group with base 5:**
$$
5^{2x - 1} - 5^{2x}
$$
... | stop | null | [
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2 | 24 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n7.109. $5^{2 x-1}+2^{2 x}-5^{2 x}+2^{2 x+2}=0$.\n\nRemember to put your answer on its own line after \"Answer:\".",
... | 7.109. $5^{2 x-1}+2^{2 x}-5^{2 x}+2^{2 x+2}=0$. | math_dapo | 1 | {
"index": 24,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 1,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-numinamath1.5_olympiads",
"prompt_style": "dapo_original"
} | 7 | We are given the equation:
$$
5^{2x - 1} + 2^{2x} - 5^{2x} + 2^{2x + 2} = 0
$$
### Step 1: Simplify the terms
First, look at the powers of 5 and 2 separately.
#### For the powers of 5:
- $5^{2x - 1}$ is part of the expression.
- $-5^{2x}$ is also part of the expression.
We can factor out $5^{2x}$ from those two ter... | stop | null | [
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3 | 15 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThere is only one set of five prime numbers that form an arithmetic sequence with a common difference of 6. What is t... | There is only one set of five prime numbers that form an arithmetic sequence with a common difference of 6. What is the sum of those five prime numbers? | math_dapo | 85 | {
"index": 15,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 0 | We are given that there is **only one set of five prime numbers** that form an **arithmetic sequence** with a **common difference of 6**. We are to find the **sum** of those five primes.
---
### Step 1: Understand the problem
An **arithmetic sequence** with a common difference of 6 means the numbers are of the form:
... | stop | null | [
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"temperature": 1,
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3 | 15 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThere is only one set of five prime numbers that form an arithmetic sequence with a common difference of 6. What is t... | There is only one set of five prime numbers that form an arithmetic sequence with a common difference of 6. What is the sum of those five prime numbers? | math_dapo | 85 | {
"index": 15,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 1 | We are asked to find **one set of five prime numbers** that form an **arithmetic sequence** with a **common difference of 6**, and then **sum those five primes**.
---
### Step 1: Understand the structure of the sequence
An arithmetic sequence with common difference 6 means:
- The five numbers are of the form:
$$
... | stop | null | [
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3 | 15 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThere is only one set of five prime numbers that form an arithmetic sequence with a common difference of 6. What is t... | There is only one set of five prime numbers that form an arithmetic sequence with a common difference of 6. What is the sum of those five prime numbers? | math_dapo | 85 | {
"index": 15,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 2 | We are looking for **five prime numbers** that form an **arithmetic sequence** with a **common difference of 6**. That means the five primes will be:
$$
p, p+6, p+12, p+18, p+24
$$
We need to find a value of **prime number $ p $** such that all five numbers in the sequence are **prime**.
---
### Step 1: Try small p... | stop | null | [
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3 | 15 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThere is only one set of five prime numbers that form an arithmetic sequence with a common difference of 6. What is t... | There is only one set of five prime numbers that form an arithmetic sequence with a common difference of 6. What is the sum of those five prime numbers? | math_dapo | 85 | {
"index": 15,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 3 | We are given that there is only **one set of five prime numbers** that form an **arithmetic sequence with a common difference of 6**. Our goal is to find the **sum of those five primes**.
---
### Step 1: Understand the problem
An arithmetic sequence with common difference 6 has the form:
$$
a, a+6, a+12, a+18, a+24... | stop | null | [
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3 | 15 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThere is only one set of five prime numbers that form an arithmetic sequence with a common difference of 6. What is t... | There is only one set of five prime numbers that form an arithmetic sequence with a common difference of 6. What is the sum of those five prime numbers? | math_dapo | 85 | {
"index": 15,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 4 | We are given that there is only **one set of five prime numbers** that form an **arithmetic sequence** with a **common difference of 6**.
Let’s denote the five primes in the arithmetic sequence as:
$$
p, p+6, p+12, p+18, p+24
$$
Each of these values must be a **prime number**. Our task is to find the value of $ p $ ... | stop | null | [
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3 | 15 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThere is only one set of five prime numbers that form an arithmetic sequence with a common difference of 6. What is t... | There is only one set of five prime numbers that form an arithmetic sequence with a common difference of 6. What is the sum of those five prime numbers? | math_dapo | 85 | {
"index": 15,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 5 | We are given that there is **only one set of five prime numbers** that form an **arithmetic sequence with a common difference of 6**. Our goal is to find this set of five primes and compute their **sum**.
---
### Step 1: Understand the structure of the sequence
An arithmetic sequence with a common difference of 6 ha... | stop | null | [
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"temperature": 1,
"thinking": false,
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} | 1 | 1 | 85 | 85 | answer | null |
3 | 15 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThere is only one set of five prime numbers that form an arithmetic sequence with a common difference of 6. What is t... | There is only one set of five prime numbers that form an arithmetic sequence with a common difference of 6. What is the sum of those five prime numbers? | math_dapo | 85 | {
"index": 15,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 6 | We are given that there is **only one set of five prime numbers** that form an **arithmetic sequence** with a **common difference of 6**. We are to find the **sum** of those five primes.
---
### Step 1: Understand the structure of the sequence
An arithmetic sequence with common difference 6 would look like:
$$
a, a... | stop | null | [
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"temperature": 1,
"thinking": false,
"top_k": -1,
"top_p": 1
} | 1 | 1 | 85 | 85 | answer | null |
3 | 15 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThere is only one set of five prime numbers that form an arithmetic sequence with a common difference of 6. What is t... | There is only one set of five prime numbers that form an arithmetic sequence with a common difference of 6. What is the sum of those five prime numbers? | math_dapo | 85 | {
"index": 15,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 7 | We are told that there is only **one set of five prime numbers** that form an **arithmetic sequence** with a **common difference of 6**.
Let’s denote the five primes in arithmetic sequence as:
$$
p, p + 6, p + 12, p + 18, p + 24
$$
We need to find a prime number $ p $ such that all five terms are prime.
---
### St... | stop | null | [
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} | 1 | 1 | 85 | 85 | answer | null |
4 | 9 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the positive difference between $\\frac{8^2 - 8^2}{8}$ and $\\frac{8^2 \\times 8^2}{8}$?\n\nRemember to put yo... | What is the positive difference between $\frac{8^2 - 8^2}{8}$ and $\frac{8^2 \times 8^2}{8}$? | math_dapo | 512 | {
"index": 9,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 0 | We are asked to find the **positive difference** between two expressions:
1. $\frac{8^2 - 8^2}{8}$
2. $\frac{8^2 \times 8^2}{8}$
---
**Step 1: Simplify the first expression**
$$
\frac{8^2 - 8^2}{8} = \frac{64 - 64}{8} = \frac{0}{8} = 0
$$
---
**Step 2: Simplify the second expression**
$$
\frac{8^2 \times 8^2}{8}... | stop | null | [
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"temperature": 1,
"thinking": false,
"top_k": -1,
"top_p": 1
} | 1 | 1 | 512 | 512 | answer | null |
4 | 9 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the positive difference between $\\frac{8^2 - 8^2}{8}$ and $\\frac{8^2 \\times 8^2}{8}$?\n\nRemember to put yo... | What is the positive difference between $\frac{8^2 - 8^2}{8}$ and $\frac{8^2 \times 8^2}{8}$? | math_dapo | 512 | {
"index": 9,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 1 | We are asked to find the **positive difference** between two expressions:
1. $\frac{8^2 - 8^2}{8}$
2. $\frac{8^2 \times 8^2}{8}$
---
### Step 1: Simplify the first expression
$$
\frac{8^2 - 8^2}{8} = \frac{64 - 64}{8} = \frac{0}{8} = 0
$$
---
### Step 2: Simplify the second expression
$$
\frac{8^2 \times 8^2}{8}... | stop | null | [
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"model": "Qwen/Qwen3-4B",
"seed": 42,
"temperature": 1,
"thinking": false,
"top_k": -1,
"top_p": 1
} | 1 | 1 | 512 | 512 | answer | null |
4 | 9 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the positive difference between $\\frac{8^2 - 8^2}{8}$ and $\\frac{8^2 \\times 8^2}{8}$?\n\nRemember to put yo... | What is the positive difference between $\frac{8^2 - 8^2}{8}$ and $\frac{8^2 \times 8^2}{8}$? | math_dapo | 512 | {
"index": 9,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 2 | We are asked to find the **positive difference** between two expressions:
1. $\frac{8^2 - 8^2}{8}$
2. $\frac{8^2 \times 8^2}{8}$
---
### Step 1: Evaluate the first expression
$$
\frac{8^2 - 8^2}{8}
$$
Since $8^2 = 64$, this becomes:
$$
\frac{64 - 64}{8} = \frac{0}{8} = 0
$$
---
### Step 2: Evaluate the second e... | stop | null | [
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"model": "Qwen/Qwen3-4B",
"seed": 42,
"temperature": 1,
"thinking": false,
"top_k": -1,
"top_p": 1
} | 1 | 1 | 512 | 512 | answer | null |
4 | 9 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the positive difference between $\\frac{8^2 - 8^2}{8}$ and $\\frac{8^2 \\times 8^2}{8}$?\n\nRemember to put yo... | What is the positive difference between $\frac{8^2 - 8^2}{8}$ and $\frac{8^2 \times 8^2}{8}$? | math_dapo | 512 | {
"index": 9,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 3 | We are asked to find the **positive difference** between two expressions:
1. $\frac{8^2 - 8^2}{8}$
2. $\frac{8^2 \times 8^2}{8}$
---
### Step 1: Evaluate the first expression
$$
\frac{8^2 - 8^2}{8}
$$
Since $8^2 = 64$, we have:
$$
\frac{64 - 64}{8} = \frac{0}{8} = 0
$$
---
### Step 2: Evaluate the second expres... | stop | null | [
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"seed": 42,
"temperature": 1,
"thinking": false,
"top_k": -1,
"top_p": 1
} | 1 | 1 | 512 | 512 | answer | null |
4 | 9 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the positive difference between $\\frac{8^2 - 8^2}{8}$ and $\\frac{8^2 \\times 8^2}{8}$?\n\nRemember to put yo... | What is the positive difference between $\frac{8^2 - 8^2}{8}$ and $\frac{8^2 \times 8^2}{8}$? | math_dapo | 512 | {
"index": 9,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 4 | We are asked to find the **positive difference** between two expressions:
1. $\frac{8^2 - 8^2}{8}$
2. $\frac{8^2 \times 8^2}{8}$
---
### Step 1: Evaluate the first expression
$$
\frac{8^2 - 8^2}{8}
$$
Note that $8^2 = 64$, so:
$$
\frac{64 - 64}{8} = \frac{0}{8} = 0
$$
---
### Step 2: Evaluate the second express... | stop | null | [
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"seed": 42,
"temperature": 1,
"thinking": false,
"top_k": -1,
"top_p": 1
} | 1 | 1 | 512 | 512 | answer | null |
4 | 9 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the positive difference between $\\frac{8^2 - 8^2}{8}$ and $\\frac{8^2 \\times 8^2}{8}$?\n\nRemember to put yo... | What is the positive difference between $\frac{8^2 - 8^2}{8}$ and $\frac{8^2 \times 8^2}{8}$? | math_dapo | 512 | {
"index": 9,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 5 | We are asked to find the **positive difference** between two expressions:
1. $\frac{8^2 - 8^2}{8}$
2. $\frac{8^2 \times 8^2}{8}$
---
### Step 1: Simplify the first expression
$$
\frac{8^2 - 8^2}{8}
$$
Note that $8^2 = 64$, so:
$$
\frac{64 - 64}{8} = \frac{0}{8} = 0
$$
---
### Step 2: Simplify the second express... | stop | null | [
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4 | 9 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the positive difference between $\\frac{8^2 - 8^2}{8}$ and $\\frac{8^2 \\times 8^2}{8}$?\n\nRemember to put yo... | What is the positive difference between $\frac{8^2 - 8^2}{8}$ and $\frac{8^2 \times 8^2}{8}$? | math_dapo | 512 | {
"index": 9,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 6 | We are asked to find the **positive difference** between two expressions:
$$
\frac{8^2 - 8^2}{8} \quad \text{and} \quad \frac{8^2 \times 8^2}{8}
$$
---
**Step 1: Simplify the first expression**
$$
\frac{8^2 - 8^2}{8} = \frac{64 - 64}{8} = \frac{0}{8} = 0
$$
---
**Step 2: Simplify the second expression**
$$
\frac... | stop | null | [
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} | 1 | 1 | 512 | 512 | answer | null |
4 | 9 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the positive difference between $\\frac{8^2 - 8^2}{8}$ and $\\frac{8^2 \\times 8^2}{8}$?\n\nRemember to put yo... | What is the positive difference between $\frac{8^2 - 8^2}{8}$ and $\frac{8^2 \times 8^2}{8}$? | math_dapo | 512 | {
"index": 9,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 7 | We are asked to find the **positive difference** between two expressions:
$$
\frac{8^2 - 8^2}{8} \quad \text{and} \quad \frac{8^2 \times 8^2}{8}
$$
---
### Step 1: Simplify the first expression
$$
\frac{8^2 - 8^2}{8} = \frac{64 - 64}{8} = \frac{0}{8} = 0
$$
---
### Step 2: Simplify the second expression
$$
\frac... | stop | null | [
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} | 1 | 1 | 512 | 512 | answer | null |
5 | 5 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA certain circle's area is $x$ square units, and its circumference is $y$ units. The value of $x + y$ is $80\\pi$. Wha... | A certain circle's area is $x$ square units, and its circumference is $y$ units. The value of $x + y$ is $80\pi$. What is the radius of the circle, in units? | math_dapo | 8 | {
"index": 5,
"model_difficulty": {
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"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 0 | We are given that the **area** of a circle is $ x $ square units and the **circumference** is $ y $ units. We are also told that:
$$
x + y = 80\pi
$$
We are to **find the radius** of the circle. Let the radius be $ r $.
---
### Step 1: Express $ x $ and $ y $ in terms of $ r $
- Area of a circle:
$$
x = \pi ... | stop | null | [
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5 | 5 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA certain circle's area is $x$ square units, and its circumference is $y$ units. The value of $x + y$ is $80\\pi$. Wha... | A certain circle's area is $x$ square units, and its circumference is $y$ units. The value of $x + y$ is $80\pi$. What is the radius of the circle, in units? | math_dapo | 8 | {
"index": 5,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 1 | We are given that the **area** of a circle is $ x $ square units, and its **circumference** is $ y $ units. It is also given that:
$$
x + y = 80\pi
$$
Let the **radius** of the circle be $ r $.
---
### Step 1: Express area and circumference in terms of $ r $
The **area** of a circle is:
$$
x = \pi r^2
$$
The **c... | stop | null | [
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5 | 5 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA certain circle's area is $x$ square units, and its circumference is $y$ units. The value of $x + y$ is $80\\pi$. Wha... | A certain circle's area is $x$ square units, and its circumference is $y$ units. The value of $x + y$ is $80\pi$. What is the radius of the circle, in units? | math_dapo | 8 | {
"index": 5,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 2 | We are given:
- The **area** of a circle is $ x = \pi r^2 $
- The **circumference** of a circle is $ y = 2\pi r $
- The sum of the area and circumference is:
$$
x + y = 80\pi
$$
### Step 1: Substitute the formulas into the equation
$$
\pi r^2 + 2\pi r = 80\pi
$$
### Step 2: Divide both sides of the equation... | stop | null | [
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5 | 5 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA certain circle's area is $x$ square units, and its circumference is $y$ units. The value of $x + y$ is $80\\pi$. Wha... | A certain circle's area is $x$ square units, and its circumference is $y$ units. The value of $x + y$ is $80\pi$. What is the radius of the circle, in units? | math_dapo | 8 | {
"index": 5,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 3 | We are given that the **area** of a circle is $ x $ square units, its **circumference** is $ y $ units, and the **sum** $ x + y = 80\pi $. We are to find the **radius** of the circle.
---
### Step 1: Write formulas for area and circumference
Recall the formulas:
- **Area of a circle:**
$$
x = \pi r^2
$$
- ... | stop | null | [
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5 | 5 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA certain circle's area is $x$ square units, and its circumference is $y$ units. The value of $x + y$ is $80\\pi$. Wha... | A certain circle's area is $x$ square units, and its circumference is $y$ units. The value of $x + y$ is $80\pi$. What is the radius of the circle, in units? | math_dapo | 8 | {
"index": 5,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 4 | We are given that the **area** of a circle is $ x $, the **circumference** is $ y $, and $ x + y = 80\pi $. We are to find the **radius** of the circle.
---
### Step 1: Recall the formulas
- **Area** of a circle:
$$
x = \pi r^2
$$
- **Circumference** of a circle:
$$
y = 2\pi r
$$
---
### Step 2: Add... | stop | null | [
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5 | 5 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA certain circle's area is $x$ square units, and its circumference is $y$ units. The value of $x + y$ is $80\\pi$. Wha... | A certain circle's area is $x$ square units, and its circumference is $y$ units. The value of $x + y$ is $80\pi$. What is the radius of the circle, in units? | math_dapo | 8 | {
"index": 5,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
},
"original_data_source": "train-math-deepscaler",
"prompt_style": "dapo_original"
} | 5 | We are given:
- The **area** of a circle is $ x = \pi r^2 $
- The **circumference** of a circle is $ y = 2\pi r $
- And we are told that $ x + y = 80\pi $
Let’s set up the equation using the expressions for $ x $ and $ y $:
$$
\pi r^2 + 2\pi r = 80\pi
$$
Divide both sides of the equation by $ \pi $ to simplify:
$$... | stop | null | [
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"seed": 42,
"temperature": 1,
"thinking": false,
"top_k": -1,
"top_p": 1
} | 1 | 1 | 8 | 8 | answer | null |
End of preview. Expand in Data Studio
Qwen3-4B Nonthinking Skywork Math Rollouts
Rollouts generated by Qwen/Qwen3-4B in nonthinking mode. Answers are verified with
math-verify==0.9.0 after extracting the final Answer: or \boxed{} value. Bare LaTeX and text answers are retried inside a math environment before verify.
- Rows: 215,040
- Prompt groups: 26,880
- Samples per prompt: 8
- Correct rows: 92,497
- Overall success rate: 0.430139
Each row contains binary reward, the success fraction across all samples sharing the
same prompt_id in group_success_rate, and the parsed gold/predicted answers for auditing.
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