conversations listlengths 2 2 | question stringlengths 63 1.03k ⌀ | source stringclasses 3
values | id int64 23.6k 37.8k ⌀ | 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 |
|---|---|---|---|---|---|---|---|---|---|---|
[
{
"from": "user",
"value": "8. A uniform cube die has the numbers $1,2, \\cdots, 6$ marked on its faces. Each time two identical dice are rolled, the sum of the numbers on the top faces is the point value of that roll. What is the probability that the product of the 3 point values obtained from 3 rolls is d... | 8. A uniform cube die has the numbers $1,2, \cdots, 6$ marked on its faces. Each time two identical dice are rolled, the sum of the numbers on the top faces is the point value of that roll. What is the probability that the product of the 3 point values obtained from 3 rolls is divisible by 14? (Express your answer as a... | 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": "8. A uniform cube die has the n... | original | [
"To determine the probability that the product of the three point values obtained from rolling two dice three times is divisible by 14, we need to ensure that the product includes both factors of 2 and 7.\n\n### Step-by-Step Solution:\n\n1. **Understanding the Problem:**\n - We roll two six-sided dice three times... | [
false,
false
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"",
""
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[
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"value": "In a fruit shop, Jaime noticed that an orange costs the same as half an apple plus half a real, and he also noticed that a third of an apple costs the same as a quarter of an orange plus half a real. With the value of 5 oranges plus 5 reals, how many apples can Jaime buy?\n\n#"
... | In a fruit shop, Jaime noticed that an orange costs the same as half an apple plus half a real, and he also noticed that a third of an apple costs the same as a quarter of an orange plus half a real. With the value of 5 oranges plus 5 reals, how many apples can Jaime buy?
# | 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": "In a fruit shop, Jaime noticed ... | original | [
"Let's denote:\n- The cost of one orange as \\( O \\),\n- The cost of one apple as \\( A \\),\n- The cost of one real as \\( R \\).\n\nFrom the problem, we have two equations based on the given information:\n\n1. An orange costs the same as half an apple plus half a real:\n\\[ O = \\frac{1}{2}A + \\frac{1}{2}R \\]\... | [
false,
false
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"",
""
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"model_name": "hosted_vll... | {
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[
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"value": "283. Find a number of the form $7 x 36 y 5$, divisible by 1375."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this problem here: Find a number of the form 7x36y5 that's divisible by 1375. Hmm, let's break this down. First, I need to figure out what the... | 283. Find a number of the form $7 x 36 y 5$, divisible by 1375. | 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": "283. Find a number of the form ... | original | [
"To find a number of the form \\(7x36y5\\) that is divisible by 1375, we need to consider the prime factorization of 1375. The prime factorization of 1375 is:\n\n\\[ 1375 = 5^3 \\times 11 \\]\n\nThis means the number must be divisible by both \\(125\\) (which is \\(5^3\\)) and \\(11\\).\n\nFirst, let's check divisi... | [
false,
false
] | [
"",
""
] | {
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"model_name": "hosted_vll... | {
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[
{
"from": "user",
"value": "Which of the following statements is correct?\n\nA: Conduct a comprehensive survey to understand the sleep situation of middle school students in Changsha\n\nB: The mode of a set of data $-1$, $2$, $5$, $5$, $7$, $7$, $4$ is $7$\n\nC: If the probability of precipitation tomorrow ... | Which of the following statements is correct?
A: Conduct a comprehensive survey to understand the sleep situation of middle school students in Changsha
B: The mode of a set of data $-1$, $2$, $5$, $5$, $7$, $7$, $4$ is $7$
C: If the probability of precipitation tomorrow is $90\%$, then it will definitely rain tomorr... | 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": "Which of the following statemen... | original | [
"Let's analyze each statement one by one:\n\n**Statement A:** \"Conduct a comprehensive survey to understand the sleep situation of middle school students in Changsha\"\n- This statement describes an action (conducting a survey) rather than a mathematical or logical fact. It cannot be evaluated as true or false bas... | [
false,
false
] | [
"",
""
] | {
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"top_p": 0.8
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"model_name": "hosted_vll... | {
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[
{
"from": "user",
"value": "A polynomial $P$ of degree $n \\in \\mathbb{N}$ satisfies:\n\n$$\n\\text { for } k=0,1, \\ldots, n, P(k)=\\frac{k}{k+1}\n$$\n\nDetermine $P(n+1)$.\n\nHint: Consider looking at $(X+1) P$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to figure out the v... | A polynomial $P$ of degree $n \in \mathbb{N}$ satisfies:
$$
\text { for } k=0,1, \ldots, n, P(k)=\frac{k}{k+1}
$$
Determine $P(n+1)$.
Hint: Consider looking at $(X+1) P$. | 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": "A polynomial $P$ of degree $n \... | original | [
"To determine \\( P(n+1) \\), we start by considering the given conditions and the hint provided. We know that the polynomial \\( P \\) of degree \\( n \\) satisfies:\n\\[ P(k) = \\frac{k}{k+1} \\quad \\text{for} \\quad k = 0, 1, \\ldots, n. \\]\n\nDefine a new polynomial \\( Q(x) = (x+1)P(x) - x \\). This polynomi... | [
false,
false
] | [
"",
""
] | {
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"model_name": "hosted_vll... | {
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[
{
"from": "user",
"value": "Given \\\\(α,β∈(0, \\dfrac {π}{2})\\\\), \\\\(\\cos (α- \\dfrac {β}{2})= \\dfrac { \\sqrt {3}}{2}\\\\), \\\\(\\sin ( \\dfrac {α}{2}-β)=- \\dfrac {1}{2}\\\\), find the value of \\\\(α+β\\\\)."
},
{
"from": "assistant",
"value": "<think>\nOkay, let's try to tackle this ... | Given \\(α,β∈(0, \dfrac {π}{2})\\), \\(\cos (α- \dfrac {β}{2})= \dfrac { \sqrt {3}}{2}\\), \\(\sin ( \dfrac {α}{2}-β)=- \dfrac {1}{2}\\), find the value of \\(α+β\\). | 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 \\\\(α,β∈(0, \\dfrac {π}{... | original | [
"To find the value of \\(α + β\\), we start by analyzing the given trigonometric equations.\n\nFirst, consider the equation:\n\\[\n\\cos \\left( α - \\frac{β}{2} \\right) = \\frac{\\sqrt{3}}{2}\n\\]\nThe cosine function equals \\(\\frac{\\sqrt{3}}{2}\\) at angles \\(\\pm \\frac{\\pi}{6} + 2k\\pi\\) for any integer ... | [
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": "If $\\tan\\theta=2$, then the value of $$\\frac {\\sin\\theta\\cos\\theta}{1+\\sin^{2}\\theta }$$ is ( )\nA: $-\\frac {1}{3}$\nB: $\\frac {1}{3}$\nC: $-\\frac {2}{9}$\nD: $\\frac {2}{9}$"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. I need to find ... | If $\tan\theta=2$, then the value of $$\frac {\sin\theta\cos\theta}{1+\sin^{2}\theta }$$ is ( )
A: $-\frac {1}{3}$
B: $\frac {1}{3}$
C: $-\frac {2}{9}$
D: $\frac {2}{9}$ | 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 $\\tan\\theta=2$, then the v... | original | [
"To find the value of \\(\\frac{\\sin\\theta\\cos\\theta}{1 + \\sin^2\\theta}\\) given that \\(\\tan\\theta = 2\\), we can proceed as follows:\n\nFirst, recall that \\(\\tan\\theta = \\frac{\\sin\\theta}{\\cos\\theta} = 2\\). This implies \\(\\sin\\theta = 2\\cos\\theta\\).\n\nWe also know that \\(\\sin^2\\theta + ... | [
false,
false
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"",
""
] | {
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"model_name": "hosted_vll... | {
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"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
[
{
"from": "user",
"value": "When two dice are rolled, the numbers facing up are $m$ and $n$, respectively. The probability that the complex number $(m+ni)(n-mi)$ is a real number is ( ).\n\nA: $\\dfrac{1}{3}$\n\nB: $\\dfrac{1}{4}$\n\nC: $\\dfrac{1}{6}$\n\nD: $\\dfrac{1}{12}$"
},
{
"from": "assistant... | When two dice are rolled, the numbers facing up are $m$ and $n$, respectively. The probability that the complex number $(m+ni)(n-mi)$ is a real number is ( ).
A: $\dfrac{1}{3}$
B: $\dfrac{1}{4}$
C: $\dfrac{1}{6}$
D: $\dfrac{1}{12}$ | 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": "When two dice are rolled, the n... | original | [
"To determine the probability that the complex number \\((m+ni)(n-mi)\\) is a real number when \\(m\\) and \\(n\\) are the outcomes of rolling two dice, we start by simplifying the expression.\n\nFirst, let's expand the product:\n\\[\n(m + ni)(n - mi) = mn - m^2 i + n^2 i - nmi^2.\n\\]\nSince \\(i^2 = -1\\), this b... | [
false,
false
] | [
"",
""
] | {
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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": "Suppose that a parabola has vertex $\\left(\\tfrac{1}{4},-\\tfrac{9}{8}\\right)$, and equation $y=ax^2+bx+c$, where $a>0$ and $a+b+c$ is an integer. The minimum possible value of $a$ can be written as $\\tfrac{p}{q},$ where $p$ and $q$ are relatively prime positive integers. Find... | Suppose that a parabola has vertex $\left(\tfrac{1}{4},-\tfrac{9}{8}\right)$, and equation $y=ax^2+bx+c$, where $a>0$ and $a+b+c$ is an integer. The minimum possible value of $a$ can be written as $\tfrac{p}{q},$ where $p$ and $q$ are relatively prime positive integers. Find $p+q$. | 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": "Suppose that a parabola has ver... | original | [
"Given the vertex form of a parabola \\( y = a(x-h)^2 + k \\), we know the vertex is at \\( (h,k) = \\left( \\frac{1}{4}, -\\frac{9}{8} \\right) \\). Thus, the equation becomes:\n\\[ y = a \\left( x - \\frac{1}{4} \\right)^2 - \\frac{9}{8}. \\]\n\nExpanding this, we get:\n\\[ y = a \\left( x^2 - \\frac{1}{2}x + \\f... | [
false,
false
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"",
""
] | {
"api_url": "http://10.32.36.225:9080/v1",
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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": "23. As shown in the figure, in square $A B C D$, $E$ is the midpoint of side $B C$. The square is folded so that point $A$ coincides with point $E$, and the fold line is $M N$. If the area of the square is 64, then the area of trapezoid $A D M N$ is $\\qquad$."
},
{
"from... | 23. As shown in the figure, in square $A B C D$, $E$ is the midpoint of side $B C$. The square is folded so that point $A$ coincides with point $E$, and the fold line is $M N$. If the area of the square is 64, then the area of trapezoid $A D M N$ is $\qquad$. | 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": "23. As shown in the figure, in ... | original | [
"First, we determine the side length of the square \\(ABCD\\). Given the area of the square is 64, we find:\n\\[ \\text{Side length} = \\sqrt{64} = 8. \\]\n\nSince \\(E\\) is the midpoint of side \\(BC\\), its coordinates if we place the square on a coordinate plane with \\(A = (0, 8)\\), \\(B = (8, 8)\\), \\(C = (... | [
false,
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": 2
} |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given the set \\( A = \\{ x \\mid \\log_{a} (a x - 1) > 1 \\} \\). If \\( 3 \\in A \\), then what is the range of values for \\( a \\)?"
},
{
"from": "assistant",
"value": "<think>\nOkay, let me try to figure out this probl... | Given the set \( A = \{ x \mid \log_{a} (a x - 1) > 1 \} \). If \( 3 \in A \), then what is the range of values for \( a \)? | 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 range of values for \\( a \\) given that \\( 3 \\in A \\), we start by substituting \\( x = 3 \\) into the inequality defining the set \\( A \\).\n\nThe inequality is:\n\\[ \\log_{a} (a x - 1) > 1. \\]\n\nSubstituting \\( x = 3 \\):\n\\[ \\log_{a} (3a - 1) > 1. \\]\n\nThis can be rewritten using t... | [
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
} |
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