conversations listlengths 2 2 | question stringlengths 47 567 ⌀ | source stringclasses 1
value | id int64 1.96k 34.2k ⌀ | prompt listlengths 2 2 | 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": "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\\) (a number in base 6), we need to first convert this number from base 6 to base 10.\n\nThe base 6 number \\(100111011_6\\) can be expanded as:\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 ... | [
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... | original | [
"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 \\( f(x) = \\frac{4}{x-3} + x \\). We use the quotient rule and the power rule to differentiate it.\n \\[\n f'(x) = -\\fr... | [
false,
false
] | [
"",
""
] | {
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"top_p": 0.8
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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 $... | original | [
"To find the length of segment \\( MN \\) in the given rhombus \\( ABCD \\), we start by noting some properties of a rhombus:\n\n1. All sides are equal.\n2. Diagonals bisect each other at right angles.\n\nGiven:\n- The length of diagonal \\( AC = 12 \\).\n- Point \\( P \\) divides \\( AC \\) in the ratio \\( AP : P... | [
false,
false
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"",
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
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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",
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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... | original | [
"To determine the values of \\(a\\) and \\(b\\) such that the function \\(f(x) = ax^2 + (b-3)x + 3\\) is an even function over the interval \\(x \\in [2a-3, 4-a]\\), we need to follow these steps:\n\n1. **Identify properties of even functions:**\n An even function satisfies \\(f(-x) = f(x)\\). For a quadratic fun... | [
false,
false
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"",
""
] | {
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"top_p": 0.8
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"model_name": "hosted_vll... | {
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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 solve this problem, we start by using the given condition \\( f(1+x) = -f(1-x) \\).\n\nGiven:\n\\[ f(x) = (x + a)^3 \\]\n\nFirst, substitute \\( x+1 \\) into \\( f(x) \\):\n\\[ f(1+x) = ((1+x) + a)^3 = (x + 1 + a)^3 \\]\n\nNext, substitute \\( 1-x \\) into \\( f(x) \\):\n\\[ f(1-x) = ((1-x) + a)^3 = (1 - x + a)... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
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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": 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 \\( ... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
"backend": "litellm",
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"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 how many children attended the party and subsequently determine the value of \\(x\\), let's break down the problem:\n\n1. **Total Attendees**: There were 120 people at the party.\n\n2. **Men Attending**: \\(\\frac{1}{3}\\) of the attendees are men.\n - Number of men = \\(\\frac{1}{3} \\times 120 = 40\\).... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
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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": 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 every set of three consecutive numbers has a product equal to \\( n \\), let's denote the integers placed at the points 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 \\quad... | [
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 | [
"Given the conditions:\n1. \\( f(-x) = f(x) \\), meaning \\( f \\) is an even function.\n2. For any distinct real numbers \\( x_1, x_2 \\in [0, +\\infty) \\), \\(\\frac{f(x_1) - f(x_2)}{x_1 - x_2} < 0\\), which means \\( f \\) is strictly decreasing on \\( [0, +\\infty) \\).\n\nWe need to find the range of \\( m \\... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
"backend": "litellm",
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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": 2
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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... | original | [
"To prove that every random function \\(X = (X_t)_{t \\in T}\\) is a stochastic process and vice versa, we need to understand the definitions and properties involved.\n\n1. **Definition of a Stochastic Process**: A stochastic process is a collection of random variables indexed by a set \\(T\\). Formally, it is a fa... | [
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 need to consider the worst-case scenario where we avoid forming pairs for as long as possible.\n\nFirst, let's understand what it means to have 10 matching pairs:\n- Each pair consists of 2 socks.\n- Therefore, 10 pairs req... | [
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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