conversations listlengths 2 2 | question stringlengths 12 5.64k ⌀ | source stringclasses 8
values | id int64 43 50k ⌀ | prompt listlengths 2 2 | answer stringlengths 1 712 ⌀ | 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Find [the decimal form of] the largest prime divisor of $100111011_6$.\n"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the largest prime divisor of the number 100111011 in base 6, converted to decima... | Find [the decimal form of] the largest prime divisor of $100111011_6$.
| 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... | 181 | rephrase | [
"Rewritten Question: Find the decimal form of the largest prime divisor of \\(100111011_6\\).\n\nStep 1: Convert \\(100111011_6\\) from base-6 to base-10.\n\\[100111011_6 = 1 \\cdot 6^8 + 0 \\cdot 6^7 + 0 \\cdot 6^6 + 1 \\cdot 6^5 + 1 \\cdot 6^4 + 1 \\cdot 6^3 + 0 \\cdot 6^2 + 1 \\cdot 6^1 + 1 \\cdot 6^0\\]\n\nStep... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"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",
"n_responses": 2
} |
[
{
"from": "user",
"value": "The maximum value of the function $f(x)=\\frac{4}{{x-3}}+x(x＜3)$ is ( ).\n\nA: $-4$\n\nB: $1$\n\nC: $5$\n\nD: $-1$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the maximum value of the function f(x) = 4/(x - 3) + x, but only for x less than 3.... | The maximum value of the function $f(x)=\frac{4}{{x-3}}+x(x＜3)$ is ( ).
A: $-4$
B: $1$
C: $5$
D: $-1$ | 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 maximum value of the function \\( f(x) = \\frac{4}{x-3} + x \\) for \\( x < 3 \\).\n\nStep 1: To find the critical points, we need to take the derivative of \\( f(x) \\).\n\\[ f'(x) = -\\frac{4}{(x-3)^2} + 1 \\]\n\nStep 2: Set the derivative equal to zero to find the critical points.\n... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"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",
"n_responses": 2
} |
[
{
"from": "user",
"value": "5. The length of the diagonal $AC$ of the rhombus $ABCD$ with an acute angle at vertex $A$ is 12. Points $M$ and $N$ on sides $DA$ and $DC$ are the bases of the heights of the rhombus dropped from vertex $B$. The height $BM$ intersects the diagonal $AC$ at point $P$ such that $AP... | 5. The length of the diagonal $AC$ of the rhombus $ABCD$ with an acute angle at vertex $A$ is 12. Points $M$ and $N$ on sides $DA$ and $DC$ are the bases of the heights of the rhombus dropped from vertex $B$. The height $BM$ intersects the diagonal $AC$ at point $P$ such that $AP: PC = 2: 3$. Find the length of the seg... | 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... | 4 | rephrase | [
"Rewritten Question: In a rhombus \\(ABCD\\) with diagonal \\(AC = 12\\), points \\(M\\) and \\(N\\) are on sides \\(DA\\) and \\(DC\\) respectively, where \\(BM\\) and \\(BN\\) are heights from \\(B\\). The intersection of \\(BM\\) with \\(AC\\) divides \\(AC\\) in the ratio \\(2:3\\). Find the length of segment \... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"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",
"n_responses": 2
} |
[
{
"from": "user",
"value": "Given the function $f(x) = ax^2 + (b-3)x + 3$, where $x \\in [2a-3, 4-a]$ is an even function, find the value of $a+b$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the value of a + b given that the function f(x) = ax² + (b - 3)x + 3 is an eve... | Given the function $f(x) = ax^2 + (b-3)x + 3$, where $x \in [2a-3, 4-a]$ is an even function, find the value of $a+b$. | 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... | 2 | rephrase | [
"Rewritten Question: Given the function \\( f(x) = ax^2 + (b-3)x + 3 \\), where \\( x \\in [2a-3, 4-a] \\) is an even function, find the value of \\( a + b \\).\n\nTo determine if \\( f(x) \\) is an even function, we need to check that \\( f(-x) = f(x) \\). For \\( f(x) = ax^2 + (b-3)x + 3 \\):\n\n1. Calculate \\( ... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"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",
"n_responses": 2
} |
[
{
"from": "user",
"value": "If the function $f(x) = (x+a)^3$ holds true for any $x \\in \\mathbb{R}$ such that $f(1+x) = -f(1-x)$, find the value of $f(2) + f(-2)$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this problem here: the function f(x) = (x + a)^3 satisfies the equati... | If the function $f(x) = (x+a)^3$ holds true for any $x \in \mathbb{R}$ such that $f(1+x) = -f(1-x)$, find the value of $f(2) + f(-2)$. | 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... | -26 | rephrase | [
"Rewritten Question: Given \\( f(x) = (x+a)^3 \\), if \\( f(1+x) = -f(1-x) \\) for all \\( x \\in \\mathbb{R} \\), find \\( f(2) + f(-2) \\).\n\nStep 1: Substitute into the given condition.\n\\[ f(1+x) = ((1+x)+a)^3 = (1+x+a)^3 \\]\n\\[ -f(1-x) = -(1-x+a)^3 \\]\n\nSince these are equal:\n\\[ (1+x+a)^3 = -(1-x+a)^3 ... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"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",
"n_responses": 2
} |
[
{
"from": "user",
"value": "Given that the radius of circle $\\odot O$ is 6, and the distance between point $A$ and the center $O$ is 5, then the position relationship between point $A$ and circle $\\odot O$ is ( ).\n\nA: Point $A$ is outside circle $\\odot O$\n\nB: Point $A$ is inside circle $\\odot O$\n\n... | Given that the radius of circle $\odot O$ is 6, and the distance between point $A$ and the center $O$ is 5, then the position relationship between point $A$ and circle $\odot O$ is ( ).
A: Point $A$ is outside circle $\odot O$
B: Point $A$ is inside circle $\odot O$
C: Point $A$ is not inside circle $\odot O$
D: Po... | 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: Given a circle with radius 6 and center at point O, if the distance from point A to O is 5, determine the position of point A relative to the circle.\n\nStep 1: Compare the distance from point A to the center O with the radius of the circle.\n- Radius of circle = 6\n- Distance from A to O = 5\n... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"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",
"n_responses": 2
} |
[
{
"from": "user",
"value": "Out of the 120 people who attended the party, 1/3 are men while x% are women. The rest are children. How many children attended the party?\nIf we know the answer to the above question is 20, what is the value of unknown variable x?"
},
{
"from": "assistant",
"value": ... | null | tiger_math | 28,288 | [
{
"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... | 50 | rephrase | [
"Rewritten Question: \n120 people attended a party. 1/3 are men, x% are women. The rest are children. If there are 20 children, find x.\n\nStep 1: Calculate the number of men.\nNumber of men = 1/3 * 120 = 40\n\nStep 2: Determine the total number of adults (men + women).\nTotal adults = Number of men + Number of wom... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"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",
"n_responses": 2
} |
[
{
"from": "user",
"value": "For an integer $n \\ge 3$ we consider a circle with $n$ points on it.\nWe place a positive integer at each point, where the numbers are not necessary need to be different. Such placement of numbers is called [i]stable [/i] as three numbers next to always have product $n$ each oth... | For an integer $n \ge 3$ we consider a circle with $n$ points on it.
We place a positive integer at each point, where the numbers are not necessary need to be different. Such placement of numbers is called [i]stable [/i] as three numbers next to always have product $n$ each other.
For how many values of $n$ with $3 \l... | 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... | 680 | rephrase | [
"Rewritten Question: For which integers \\( n \\) from 3 to 2020 inclusive can we place positive integers around a circle such that for any three consecutive numbers, their product is \\( n \\)? How many such \\( n \\) exist?\n\nTo determine when this is possible, let's denote the numbers placed at the \\( n \\) po... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"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",
"n_responses": 2
} |
[
{
"from": "user",
"value": "Define a function $f(x)$ on $R$ such that $f(-x) = f(x)$, and for any distinct real numbers $x_{1}$, $x_{2} \\in [0,+\\infty)$, $\\frac{f(x_{1})-f(x_{2})}{x_{1}-x_{2}} < 0$ holds. If the inequality $f(2mx-\\ln x-3) \\geq 2f(3)-f(-2mx+\\ln x+3)$ always holds for $x \\in [1,3]$, wh... | Define a function $f(x)$ on $R$ such that $f(-x) = f(x)$, and for any distinct real numbers $x_{1}$, $x_{2} \in [0,+\infty)$, $\frac{f(x_{1})-f(x_{2})}{x_{1}-x_{2}} < 0$ holds. If the inequality $f(2mx-\ln x-3) \geq 2f(3)-f(-2mx+\ln x+3)$ always holds for $x \in [1,3]$, what is the range of real number $m$?
A: $[\frac... | 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: Define a function \\( f(x) \\) on \\( \\mathbb{R} \\) such that \\( f(-x) = f(x) \\), and for any distinct real numbers \\( x_1, x_2 \\in [0, +\\infty) \\), \\( \\frac{f(x_1) - f(x_2)}{x_1 - x_2} < 0 \\). If the inequality \\( f(2mx - \\ln x - 3) \\geq 2f(3) - f(-2mx + \\ln x + 3) \\) always ho... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"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",
"n_responses": 2
} |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Prove that every random function \\(X = \\left(X_{t}\\right)_{t \\in T}\\), considered as a random element taking values in the space \\((\\mathbb{R}^{T}, \\mathscr{B}(\\mathbb{R}^{T}))\\), is a stochastic process, i.e., a collection o... | Prove that every random function \(X = \left(X_{t}\right)_{t \in T}\), considered as a random element taking values in the space \((\mathbb{R}^{T}, \mathscr{B}(\mathbb{R}^{T}))\), is a stochastic process, i.e., a collection of random variables \(X_t\), and vice versa. | 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... | \text{Such equivalence is established via mutual measurability conditions between finite-dimensional projections and the product }\sigma\text{-algebra.} | rephrase | [
"Rewritten Question: Prove that a random function \\(X = (X_t)_{t \\in T}\\) is a stochastic process and that a stochastic process is equivalent to a collection of random variables \\(X_t\\).\n\nStep 1: Define a random function.\nA random function \\(X = (X_t)_{t \\in T}\\) maps each point \\(t\\) in the index set ... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"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",
"n_responses": 2
} |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. In a dark room, there are several socks of five different colors: red, green, blue, yellow, and white. In order to ensure that you can get 10 matching pairs of socks (two socks of the same color make a pair), what is the minimum number... | In a dark room, there are several socks of five different colors: red, green, blue, yellow, and white. In order to ensure that you can get 10 matching pairs of socks (two socks of the same color make a pair), what is the minimum number of socks you need to take out of the room?
(A) 23
(B) 24
(C) 25
(D) 26 | 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: To ensure getting 10 matching pairs of socks from five different colors, what is the minimum number of socks needed?\n\nStep-by-step solution:\n1. Each pair consists of 2 socks.\n2. For 10 pairs, we need \\(10 \\times 2 = 20\\) socks if all pairs were of distinct colors.\n3. However, since ther... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"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",
"n_responses": 2
} |
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