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 | [
"Rewritten Question: Find the number of roots of the equation $\\sqrt{x^2 + 12x + 36} + x + 6 = 0$.\n\nStep-by-step solution:\n1. First, simplify the expression under the square root: $x^2 + 12x + 36 = (x + 6)^2$. So the equation becomes $\\sqrt{(x + 6)^2} + x + 6 = 0$.\n2. Since $\\sqrt{(x + 6)^2} = |x + 6|$, we n... | [
false,
false
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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 | [
"Rewritten Question: Which of the following propositions about vectors is correct?\n\nA: If $|\\overrightarrow{a}| > |\\overrightarrow{b}|$ and $\\overrightarrow{a}$ is in the same direction as $\\overrightarrow{b}$, then $\\overrightarrow{a} > \\overrightarrow{b}$.\n\nB: $|\\overrightarrow{a} + \\overrightarrow{b}... | [
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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 | [
"Rewritten Question: Determine if the condition \"a > 0, and a ≠ 1\" is sufficient, necessary, or both for \"log_a(2) > 0\".\n\nStep 1: Analyze the given condition.\n- We need to check two parts of the condition:\n 1. \\(a > 0\\)\n 2. \\(a \\neq 1\\)\n\nStep 2: Analyze the requirement \"log_a(2) > 0\".\n- The log... | [
false,
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"",
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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 | [
"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 the members.\n\nStep 1: Understand the structure.\nGiven that every pair of people has exactly one mutual friend, this suggests a specific type... | [
false,
false
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"",
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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?"
},
{
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"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 | [
"Rewritten Question: Selene buys 2 instant cameras at $110 each and 3 digital photo frames at $120 each. She receives a 5% discount on all items. Calculate her total payment.\n\nStep 1: Calculate the cost of the instant cameras.\nCost of instant cameras = 2 * $110\n\nStep 2: Calculate the cost of the digital photo ... | [
false,
false
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"",
""
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"model_name": "hosted_vll... | {
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[
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"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 | [
"Rewritten Question: \nCompute the corrected coordinates for point T given its preliminary coordinates (2713.835, 1727.740) and the latitude and departure errors (\\( \\text{Lat err}_T = +0.555' \\), \\( \\text{Dep err}_T = -0.070' \\)).\n\nStep 1: Identify the preliminary coordinates of point T.\n\\( X_T = 2713.83... | [
false,
false
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"",
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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 | [
"Rewritten Question: Find all functions \\( f: \\mathbb{R} \\to \\mathbb{R} \\) such that for all \\( x \\in \\mathbb{R} \\), \\( f(x) = \\max_{y \\in \\mathbb{R}} (2xy - f(y)) \\).\n\nTo find the function \\( f \\), let's analyze the given functional equation:\n\\[ f(x) = \\max_{y \\in \\mathbb{R}} (2xy - f(y)). \... | [
false,
false
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"",
""
] | {
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"top_p": 0.8
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"model_name": "hosted_vll... | {
"backend": "litellm",
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[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Alex wrote all natural divisors of a natural number \\( n \\) on the board in ascending order. Dima erased several of the first and several of the last numbers of the resulting sequence so that 151 numbers remained. What is the maximum... | Alex wrote all natural divisors of a natural number \( n \) on the board in ascending order. Dima erased several of the first and several of the last numbers of the resulting sequence so that 151 numbers remained. What is the maximum number of these 151 divisors that could be fifth powers of natural numbers? | 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... | 31 | rephrase | [
"Rewritten Question: A natural number \\( n \\) has its natural divisors listed in ascending order. After erasing some of the first and last divisors, 151 divisors remain. What is the maximum number of these remaining divisors that can be fifth powers of natural numbers?\n\nTo solve this problem, we need to underst... | [
false,
false
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"",
""
] | {
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"chat_template_applied": true,
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"top_p": 0.8
},
"model_name": "hosted_vll... | {
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"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
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"",
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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 | ["Rewritten Question: \n10 consecutive natural numbers. Sum of last 6 = 15 + 2 * (sum of first 4). F(...TRUNCATED) | [
false,
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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) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
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