conversations listlengths 2 2 | question stringlengths 8 4.13k ⌀ | source stringclasses 8
values | id int64 3 50k ⌀ | prompt listlengths 2 2 | answer stringlengths 1 587 ⌀ | prompt_type stringclasses 1
value | model_responses__example_annotation listlengths 2 2 | model_responses__example_annotation__finish_reason_length_flags listlengths 2 2 | model_responses__example_annotation__length_partial_responses listlengths 2 2 | prompt__example_annotation__metadata dict | model_responses__example_annotation__metadata dict |
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"value": "$2 \\cdot 131$ The number of roots of the equation $\\sqrt{x^{2}+12 x+36}+x+6=0$ is\n(A) 0.\n(B) 2.\n(C) 4.\n(D) Infinitely many.\n(3rd \"Five Sheep Cup\" Junior High School Mathematics Competition, 1991)"
},
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"value": "<think>\nOkay, let me try ... | $2 \cdot 131$ The number of roots of the equation $\sqrt{x^{2}+12 x+36}+x+6=0$ is
(A) 0.
(B) 2.
(C) 4.
(D) Infinitely many.
(3rd "Five Sheep Cup" Junior High School Mathematics Competition, 1991) | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | D | rephrase_rationalized | [
"Rewritten Question: Find the number of real roots for the equation $\\sqrt{x^2 + 12x + 36} + x + 6 = 0$.\n\nStep 1: Simplify the expression under the square root. Notice that $x^2 + 12x + 36 = (x + 6)^2$. So, the equation becomes $\\sqrt{(x + 6)^2} + x + 6 = 0$.\n\nStep 2: Recognize that $\\sqrt{(x + 6)^2}$ simpli... | [
false,
false
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"",
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[
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"value": "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following propositions is correct?\n\nA: If $|\\overrightarrow{a}| > |\\overrightarrow{b}|$ and $\\overrightarrow{a}$ is in the same direction as $\\overrightarrow{b}$, then $\\overrightarrow{a} > \... | For any two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$, which of the following propositions is correct?
A: If $|\overrightarrow{a}| > |\overrightarrow{b}|$ and $\overrightarrow{a}$ is in the same direction as $\overrightarrow{b}$, then $\overrightarrow{a} > \overrightarrow{b}$.
B: $|\overrightarrow{a} + \o... | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | B | rephrase_rationalized | [
"Rewritten Question: Determine which proposition about vectors is correct among the given options.\n\nLet's analyze each option:\n\n**Option A:** If \\( |\\overrightarrow{a}| > |\\overrightarrow{b}| \\) and \\(\\overrightarrow{a}\\) is in the same direction as \\(\\overrightarrow{b}\\), then \\(\\overrightarrow{a} ... | [
false,
false
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"",
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"model_name": "hosted_vll... | {
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[
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"value": "The condition \"a > 0, and a ≠ 1\" is the ( ) condition for \"loga2 > 0\".\nA: Sufficient but not necessary condition\nB: Necessary but not sufficient condition\nC: Sufficient and necessary condition\nD: Neither sufficient nor necessary condition"
},
{
"from": "assistant"... | The condition "a > 0, and a ≠ 1" is the ( ) condition for "loga2 > 0".
A: Sufficient but not necessary condition
B: Necessary but not sufficient condition
C: Sufficient and necessary condition
D: Neither sufficient nor necessary condition | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | B | rephrase_rationalized | [
"Rewritten Question: Determine if the condition \"a > 0, and a ≠ 1\" is sufficient, necessary, or both for \"loga2 > 0\".\n\nStep 1: Analyze the condition \"a > 0, and a ≠ 1\".\n- This means \\(a\\) can be any positive number except 1.\n\nStep 2: Analyze the statement \"loga2 > 0\".\n- The logarithm \\(\\log_a 2\\)... | [
false,
false
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[
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"value": "In a group of 2017 persons, any pair of persons has exactly one common friend (other than the pair of persons). Determine the smallest possible value of the difference between the numbers of friends of the person with the most friends and the person with the least friends in such... | In a group of 2017 persons, any pair of persons has exactly one common friend (other than the pair of persons). Determine the smallest possible value of the difference between the numbers of friends of the person with the most friends and the person with the least friends in such a group. | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | 2014 | rephrase_rationalized | [
"Rewritten Question: In a group of 2017 persons, any two have exactly one mutual friend. Find the minimum difference between the maximum and minimum number of friends among these individuals.\n\nStep 1: Understand the structure.\nGiven any two people, there's exactly one other person who knows both of them. This su... | [
false,
false
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"",
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"chat_template_applied": true,
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"model_name": "hosted_vll... | {
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[
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"value": "Selene buys two instant cameras at $110 and three digital photo frames at $120 each. She gets a 5% discount on all the items she purchased. How much does she pay in all?"
},
{
"from": "assistant",
"value": "<think>\nOkay, so Selene bought two instant cameras and three... | null | tiger_math | 11,673 | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | 551 | rephrase_rationalized | [
"Rewritten Question: Selene buys two instant cameras at $110 each and three digital photo frames at $120 each. She receives a 5% discount on her total purchase. What is the total amount she pays after the discount?\n\nStep 1: Calculate the cost of the instant cameras.\nCost of instant cameras = 2 * $110\n\nStep 2: ... | [
false,
false
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"",
""
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"chat_template_applied": true,
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"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
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[
{
"from": "user",
"value": "Given the preliminary coordinates of points Q, R, S, and T, along with their latitude and departure errors, compute the corrected coordinates for point T using the corrections derived from the Compass Rule. The preliminary coordinates are:\n\n- Q: (2600.480, 1391.670)\n- R: (2379... | null | automath | 32,975 | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | (2713.905, 1727.185) | rephrase_rationalized | [
"Rewritten Question: Given the preliminary coordinates of point T as (2713.835, 1727.740) and its latitude error as +0.555' and departure error as -0.070', find the corrected coordinates of point T.\n\nStep 1: Correct the X-coordinate.\nPreliminary X-coordinate = 2713.835'\nLatitude error = +0.555'\nCorrected X-coo... | [
false,
false
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"",
""
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"model_name": "hosted_vll... | {
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[
{
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"value": "Find all functions $f:\\mathbb{R}\\rightarrow \\mathbb{R}$ such that\n$\\forall x\\in \\mathbb{R} \\ \\ f(x) = max(2xy-f(y))$ where $y\\in \\mathbb{R}$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find all functions \\( f: \\mathbb{R} \\rightarrow... | Find all functions $f:\mathbb{R}\rightarrow \mathbb{R}$ such that
$\forall x\in \mathbb{R} \ \ f(x) = max(2xy-f(y))$ where $y\in \mathbb{R}$. | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | x^2 | rephrase_rationalized | [
"Rewritten Question: Find all functions \\( f : \\mathbb{R} \\rightarrow \\mathbb{R} \\) such that for all \\( x \\in \\mathbb{R} \\), \\( f(x) = \\max(2xy - f(y)) \\).\n\nTo find the function \\( f \\), let's start by examining specific values of \\( y \\):\n\n1. **Substitute \\( y = 0 \\):**\n \\[\n f(x) = \\... | [
false,
false
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"",
""
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"n": 2,
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"top_p": 0.8
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"model_name": "hosted_vll... | {
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[{"from":"user","value":"Return your final response within \\boxed{}. Alex wrote all natural divisor(...TRUNCATED) | "Alex wrote all natural divisors of a natural number \\( n \\) on the board in ascending order. Dima(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 31 | rephrase_rationalized | ["Rewritten Question: Alex wrote all natural divisors of a natural number \\( n \\) on the board in (...TRUNCATED) | [
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"",
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] | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
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"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
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[{"from":"user","value":"In the binomial expansion of $(a+b)^n$, if the sum of the binomial coeffici(...TRUNCATED) | "In the binomial expansion of $(a+b)^n$, if the sum of the binomial coefficients of the odd terms is(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 70 | rephrase_rationalized | ["Rewritten Question: In the binomial expansion of \\((a+b)^n\\), if the sum of the binomial coeffic(...TRUNCATED) | [
false,
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"",
""
] | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
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[{"from":"user","value":"12. 10 consecutive natural numbers are arranged in ascending order. If the (...TRUNCATED) | "12. 10 consecutive natural numbers are arranged in ascending order. If the sum of the last 6 number(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 6 | rephrase_rationalized | ["Rewritten Question: 10 consecutive natural numbers are arranged in ascending order. The sum of the(...TRUNCATED) | [
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"",
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