conversations listlengths 2 2 | question stringlengths 40 3.04k ⌀ | source stringclasses 5
values | id int64 1.96k 49.6k ⌀ | prompt listlengths 2 2 | prompt_type stringclasses 4
values | 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": "Return your final response within \\boxed{}. Find [the decimal form of] the largest prime divisor of $100111011_6$.\n"
},
{
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"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 like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer.",
"role": "system"
},
{
"content": "Return your final response with... | original | [
"To find the largest prime divisor of \\( 100111011_6 \\), we first need to convert this number from base-6 to base-10.\n\nThe base-6 number \\( 100111011_6 \\) can be expanded as:\n\\[\n1 \\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 ... | [
false,
false
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"",
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
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"chat_template_applied": true,
"generation_params": {
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"n": 1,
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"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
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"model_name": "hosted_vll... | {
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[
{
"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 like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer.",
"role": "system"
},
{
"content": "The maximum value of the functi... | original | [
"To find the maximum value of the function \\( f(x) = \\frac{4}{x-3} + x \\) for \\( x < 3 \\), we need to follow these steps:\n\n1. **Find the derivative of the function**:\n The function is \\( f(x) = \\frac{4}{x-3} + x \\). We use the quotient rule and the power rule to differentiate it.\n \\[\n f'(x) = -\... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
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"n": 1,
"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 like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer.",
"role": "system"
},
{
"content": "5. The length of the diagonal $... | original | [
"To find the length of segment \\( MN \\) in the given rhombus, we need to follow a series of logical steps.\n\nFirst, let's denote the side length of the rhombus as \\( s \\). Since \\( AC \\) is the diagonal of the rhombus and its length is 12, we can use the properties of the rhombus to find the lengths of the o... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
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"generation_params": {
"chat_template_applied": true,
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"n": 1,
"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 like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer.",
"role": "system"
},
{
"content": "Given the function $f(x) = ax^2... | original | [
"To determine if \\( f(x) = ax^2 + (b-3)x + 3 \\) is an even function over the interval \\([2a-3, 4-a]\\), we need to satisfy two conditions: \n1. The function must be symmetric about the y-axis.\n2. The domain must also be symmetric about zero.\n\n### Step 1: Symmetry Condition\n\nFor a quadratic function to be ev... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
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"n": 1,
"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": "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 like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer.",
"role": "system"
},
{
"content": "If the function $f(x) = (x+a)^3... | original | [
"To determine the value of \\( f(2) + f(-2) \\), we start by analyzing the given functional equation \\( f(1+x) = -f(1-x) \\). Given that \\( f(x) = (x+a)^3 \\), we substitute this into the equation:\n\n\\[ f(1+x) = ((1+x) + a)^3 = (1 + x + a)^3 \\]\n\\[ f(1-x) = ((1-x) + a)^3 = (1 - x + a)^3 \\]\n\nThus, the equat... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
"backend": "litellm",
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"chat_template_applied": true,
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"n": 1,
"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 like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer.",
"role": "system"
},
{
"content": "Given that the radius of circle... | original | [
"To determine the position relationship between point \\( A \\) and circle \\(\\odot O\\), we need to compare the distance from point \\( A \\) to the center \\( O \\) with the radius of the circle.\n\n1. The radius of circle \\(\\odot O\\) is given as 6.\n2. The distance from point \\( A \\) to the center \\( O \\... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 1,
"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 like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer.",
"role": "system"
},
{
"content": "Out of the 120 people who atten... | original | [
"To find the number of children at the party and subsequently determine the value of \\(x\\), let's break down the problem into steps.\n\nFirst, calculate the number of men:\n- There are 120 people in total.\n- \\(\\frac{1}{3}\\) of these are men: \n\\[ \\text{Number of men} = \\frac{1}{3} \\times 120 = 40 \\]\n\nN... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
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"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 1,
"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 like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer.",
"role": "system"
},
{
"content": "For an integer $n \\ge 3$ we co... | original | [
"To determine for which values of \\( n \\) it is possible to place numbers such that any three consecutive numbers multiply to \\( n \\), let's analyze the conditions and constraints.\n\n1. **Understanding the Condition:**\n - For any three consecutive numbers \\(a_i, a_{i+1}, a_{i+2}\\) (where indices are taken... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 1,
"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 like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer.",
"role": "system"
},
{
"content": "Define a function $f(x)$ on $R$... | original | [
"To solve this problem, we need to analyze the properties of the function \\( f(x) \\). The first property given is that \\( f(-x) = f(x) \\), which means \\( f(x) \\) is an even function. The second property is that for any distinct real numbers \\( x_1, x_2 \\in [0, +\\infty) \\), \\(\\frac{f(x_1) - f(x_2)}{x_1 -... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 1,
"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 like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer.",
"role": "system"
},
{
"content": "Return your final response with... | original | [
"To prove that every random function \\(X = (X_t)_{t \\in T}\\) is a stochastic process and vice versa, we need to establish two things:\n\n1. If \\(X\\) is a stochastic process, then it is a random function.\n2. If \\(X\\) is a random function, then it is a stochastic process.\n\n### Step 1: Stochastic Process imp... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 1,
"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 like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer.",
"role": "system"
},
{
"content": "Return your final response with... | original | [
"To determine the minimum number of socks needed to guarantee at least 10 matching pairs, we must consider the worst-case scenario where we pick as many mismatched socks as possible before getting our first matching pair.\n\n1. **Worst-Case Scenario Analysis**:\n - If we pick one sock of each color, we will have ... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 1,
"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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