conversations listlengths 2 2 | question stringclasses 9
values | source stringclasses 1
value | id int64 28.3k 28.3k ⌀ | prompt listlengths 2 2 | answer stringclasses 9
values | prompt_type stringclasses 8
values | model_responses__example_annotation listlengths 1 1 | model_responses__example_annotation__finish_reason_length_flags listlengths 1 1 | model_responses__example_annotation__length_partial_responses listlengths 1 1 | 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"
},
{
"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 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... | 181 | original | [
"To find the largest prime divisor of \\(100111011_6\\) (a number in base 6), we first need to convert it to its decimal (base 10) form.\n\nThe number \\(100111011_6\\) can be expanded as follows:\n\\[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... | [
false
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""
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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... | D | original | [
"To find the maximum value of the function \\( f(x) = \\frac{4}{x-3} + x \\) for \\( x < 3 \\), we start by finding its critical points through differentiation.\n\nFirst, compute the derivative of \\( f(x) \\):\n\\[ f'(x) = -\\frac{4}{(x-3)^2} + 1. \\]\n\nSet the derivative equal to zero to find the critical points... | [
false
] | [
""
] | {
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[
{
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"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 $... | 4 | original | [
"To find the length of segment \\( MN \\), we start by analyzing the given information about the rhombus \\( ABCD \\).\n\n1. **Identify Key Properties**:\n - Since \\( ABCD \\) is a rhombus, all its sides are equal.\n - Diagonals \\( AC \\) and \\( BD \\) bisect each other at right angles.\n - Given \\( AP:PC... | [
false
] | [
""
] | {
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[
{
"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... | 2 | original | [
"To determine the value of \\(a + b\\) for the given function \\(f(x) = ax^2 + (b-3)x + 3\\), we need to use the property that \\(f(x)\\) is an even function over the interval \\([2a-3, 4-a]\\). For a function to be even, it must satisfy \\(f(-x) = f(x)\\) and its domain must be symmetric about the origin.\n\nFirst... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
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"top_p": 0.8
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"model_name": "hosted_vll... | {
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"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... | -26 | original | [
"To determine the value of \\(a\\) and subsequently find \\(f(2) + f(-2)\\), we start with the given condition:\n\\[ f(1+x) = -f(1-x). \\]\nGiven \\( f(x) = (x+a)^3 \\), substitute into the equation:\n\\[ f(1+x) = ((1+x)+a)^3 = (1+x+a)^3, \\]\nand\n\\[ f(1-x) = ((1-x)+a)^3 = (1-x+a)^3. \\]\nThus, the condition beco... | [
false
] | [
""
] | {
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"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 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... | B | original | [
"To determine the position of point \\( A \\) relative to 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 between point \\( A \\) and the center \\( O \\) is g... | [
false
] | [
""
] | {
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"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[
{
"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... | 50 | original | [
"To find the number of children and the value of \\(x\\), let's start by calculating the number of men at the party.\n\nGiven:\n- Total attendees = 120\n- Fraction of men = \\(\\frac{1}{3}\\)\n\nThe number of men can be calculated as:\n\\[ \\text{Number of men} = \\frac{1}{3} \\times 120 = 40 \\]\n\nSince the total... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
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"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": "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... | 680 | original | [
"To determine for which values of \\( n \\) (where \\( 3 \\leq n \\leq 2020 \\)) it's possible to place numbers such that any three consecutive numbers have a product equal to \\( n \\), let's denote these numbers as \\( a_1, a_2, \\ldots, a_n \\). The condition given implies:\n\n\\[ a_i \\cdot a_{i+1} \\cdot a_{i+... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
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"chat_template_applied": true,
"max_tokens": 4096,
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"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": 1
} |
[
{
"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 $R$... | D | original | [
"To solve this problem, we need to analyze the given conditions and use them to find the range of \\( m \\).\n\nFirstly, let's interpret the conditions provided:\n1. The function \\( f(x) \\) is even, i.e., \\( f(-x) = f(x) \\).\n2. For any distinct real numbers \\( x_1, x_2 \\in [0, +\\infty) \\), the condition \\... | [
false
] | [
""
] | {
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"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[
{
"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... | \text{Such equivalence is established via mutual measurability conditions between finite-dimensional projections and the product }\sigma\text{-algebra.} | original | [
"To prove that every random function \\( X = (X_t)_{t \\in T} \\) is a stochastic process, and conversely, every stochastic process can be viewed as a random function, we need to establish two main points:\n\n1. **Every random function \\( X = (X_t)_{t \\in T} \\) is a stochastic process:**\n\n - A random functio... | [
false
] | [
""
] | {
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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": 1
} |
[
{
"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 like to solve problems by understanding the problem, writing a plan, executing the plan, then giving an answer. Write a plan that when reasoned over would solve the question then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end witho... | 181 | plan_and_execute | [
"First, I'll try to understand the problem better by writing out a plan and go really deep into detail about how I should solve this.\n\n### Plan:\n\n1. **Convert the Number from Base 6 to Base 10:**\n - The given number is \\(100111011_6\\). We need to convert it to base 10.\n - To do so, we will multiply each... | [
false
] | [
""
] | {
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"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": 1
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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 understanding the problem, writing a plan, executing the plan, then giving an answer. Write a plan that when reasoned over would solve the question then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end witho... | D | plan_and_execute | [
"First, I'll try to understand the problem better by writing out a plan and go really deep into detail about how I should solve this.\n\nStep 1: Analyze the Function\nWe are given \\( f(x) = \\frac{4}{x-3} + x \\) for \\( x < 3 \\). The goal is to find its maximum value under these constraints.\n\nStep 2: Simplify ... | [
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": 1
} |
[
{
"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 understanding the problem, writing a plan, executing the plan, then giving an answer. Write a plan that when reasoned over would solve the question then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end witho... | 4 | plan_and_execute | [
"First, I'll try to understand the problem better by writing out a plan and go really deep into detail about how I should solve this.\n\n### Step-by-Step Plan:\n\n1. **Understand the Geometry**:\n - We have a rhombus \\(ABCD\\) where the diagonals bisect each other at right angles.\n - Diagonal \\(AC = 12\\).\n... | [
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": 1
} |
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