conversations listlengths 2 2 | question stringlengths 47 466 ⌀ | source stringclasses 1
value | id int64 28.3k 28.3k ⌀ | prompt listlengths 2 2 | answer stringclasses 20
values | 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... | 181 | original_rationalized | [
"To find the decimal form of the largest prime divisor of \\(100111011_6\\), we need to follow these steps:\n\n1. **Convert the base-6 number to a decimal (base-10) number**:\n The base-6 number \\(100111011_6\\) can be expanded as follows:\n \\[\n 1 \\cdot 6^8 + 0 \\cdot 6^7 + 0 \\cdot 6^6 + 1 \\cdot 6^5 + 1... | [
false,
false
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"",
""
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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... | D | original_rationalized | [
"To find the maximum value of the function \\( f(x) = \\frac{4}{x-3} + x \\) for \\( x < 3 \\), we will follow these steps:\n\n1. **Find the derivative of \\( f(x) \\):**\n The function is given by:\n \\[\n f(x) = \\frac{4}{x-3} + x\n \\]\n To differentiate, use the sum rule and the quotient rule.\n - F... | [
false,
false
] | [
"",
""
] | {
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"n": 1,
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"top_p": 0.8
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"model_name": "hosted_vll... | {
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[
{
"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 $... | 4 | original_rationalized | [
"To find the length of segment \\( MN \\), we need to carefully analyze the given information about the rhombus and use geometric properties.\n\nFirst, let's denote the side length of the rhombus as \\( s \\). Since \\( AC \\) is a diagonal of the rhombus and it has a length of 12, and knowing that the diagonals of... | [
false,
false
] | [
"",
""
] | {
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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": "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_rationalized | [
"To determine if \\( f(x) = ax^2 + (b-3)x + 3 \\) is an even function over the interval \\( x \\in [2a-3, 4-a] \\), we need to satisfy two conditions:\n1. The domain must be symmetric about zero.\n2. The function itself must satisfy \\( f(-x) = f(x) \\).\n\n### Step 1: Symmetry of the Domain\n\nFor the domain to be... | [
false,
false
] | [
"",
""
] | {
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"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... | -26 | original_rationalized | [
"To start solving the problem, we need to use the given condition \\(f(1+x) = -f(1-x)\\).\n\nGiven:\n\\[ f(x) = (x + a)^3 \\]\n\nWe substitute into the condition:\n\\[ f(1 + x) = ((1 + x) + a)^3 = (x + 1 + a)^3 \\]\n\\[ f(1 - x) = ((1 - x) + a)^3 = (-x + 1 + a)^3 \\]\n\nThe condition states:\n\\[ (x + 1 + a)^3 = -(... | [
false,
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... | {
"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... | B | original_rationalized | [
"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. **Identify given information:**\n - The radius of circle \\(\\odot O\\) is 6.\n - The distance between poin... | [
false,
false
] | [
"",
""
] | {
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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",
"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... | 50 | original_rationalized | [
"To find the number of children at the party, let's first determine the number of men and women.\n\nGiven:\n- Total attendees = 120\n- Fraction of men = \\( \\frac{1}{3} \\)\n\nNumber of men = \\( \\frac{1}{3} \\times 120 = 40 \\)\n\nLet the percentage of women be \\( x\\%\\). Then the fraction of women is \\( \\fr... | [
false,
false
] | [
"",
""
] | {
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"chat_template_applied": true,
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"n": 1,
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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",
"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... | 680 | original_rationalized | [
"To determine for which values of \\( n \\) it is possible to place numbers such that the product of any three consecutive numbers equals \\( n \\), let's denote the numbers placed at the points of the circle as \\( a_1, a_2, \\ldots, a_n \\). The condition given is:\n\n\\[ a_i \\cdot a_{i+1} \\cdot a_{i+2} = n \\]... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
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"n": 1,
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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",
"n_responses": 2
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[
{
"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_rationalized | [
"To solve the problem, we need to carefully analyze the properties of the function \\( f(x) \\).\n\nFirstly, from the condition \\( f(-x) = f(x) \\), we know that \\( f(x) \\) is an even function.\n\nSecondly, the condition \\( \\frac{f(x_1) - f(x_2)}{x_1 - x_2} < 0 \\) for any distinct real numbers \\( x_1, x_2 \\... | [
false,
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",
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[
{
"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_rationalized | [
"To prove that every random function \\( X = (X_t)_{t \\in T} \\) is a stochastic process, we need to show that it can be viewed as a single random variable taking values in the space \\((\\mathbb{R}^T, \\mathscr{B}(\\mathbb{R}^T))\\). Conversely, we need to demonstrate that any such random variable can be decompos... | [
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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