conversations listlengths 2 2 | question stringlengths 8 4.13k ⌀ | source stringclasses 8
values | id int64 3 50k ⌀ | prompt listlengths 2 2 | answer stringlengths 1 587 ⌀ | prompt_type stringclasses 1
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"value": "$2 \\cdot 131$ The number of roots of the equation $\\sqrt{x^{2}+12 x+36}+x+6=0$ is\n(A) 0.\n(B) 2.\n(C) 4.\n(D) Infinitely many.\n(3rd \"Five Sheep Cup\" Junior High School Mathematics Competition, 1991)"
},
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"value": "<think>\nOkay, let me try ... | $2 \cdot 131$ The number of roots of the equation $\sqrt{x^{2}+12 x+36}+x+6=0$ is
(A) 0.
(B) 2.
(C) 4.
(D) Infinitely many.
(3rd "Five Sheep Cup" Junior High School Mathematics Competition, 1991) | null | null | [
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"content": "$2 \\cdot 131$ The number of ro... | D | original | [
"To determine the number of roots of the equation \\(\\sqrt{x^2 + 12x + 36} + x + 6 = 0\\), we start by simplifying the expression inside the square root.\n\nFirst, notice that \\(x^2 + 12x + 36\\) can be rewritten as a perfect square:\n\\[x^2 + 12x + 36 = (x + 6)^2.\\]\nSo the equation becomes:\n\\[\\sqrt{(x + 6)^... | [
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"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"
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"content": "$2 \\cdot 131$ The number of roots of the equation $\\sqrt{x^{2}+12 x+36}+x+6=0$ is\n(A) 0.\n(B) 2.\n(C) 4.\n(D) Infinitely many.\n(3rd \"Five Sheep Cup\" Junior High School Mathematics Competition, 1991)",
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[
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"value": "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following propositions is correct?\n\nA: If $|\\overrightarrow{a}| > |\\overrightarrow{b}|$ and $\\overrightarrow{a}$ is in the same direction as $\\overrightarrow{b}$, then $\\overrightarrow{a} > \... | For any two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$, which of the following propositions is correct?
A: If $|\overrightarrow{a}| > |\overrightarrow{b}|$ and $\overrightarrow{a}$ is in the same direction as $\overrightarrow{b}$, then $\overrightarrow{a} > \overrightarrow{b}$.
B: $|\overrightarrow{a} + \overrightarrow{b}| \leq |\overrightarrow{a}| + |\overrightarrow{b}|$
C: If $\overrightarrow{a} \parallel \overrightarrow{c}$, then there exists a unique real number $k$ such that $\overrightarrow{a} = k\overrightarrow{c}$.
D: $|\overrightarrow{a} - \overrightarrow{b}| \leq |\overrightarrow{a}| - |\overrightarrow{b}|$ | 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"
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"content": "For any two vectors $\\overrigh... | B | original | [
"Let's analyze each proposition one by one:\n\n**Proposition A:** \"If \\( |\\overrightarrow{a}| > |\\overrightarrow{b}| \\) and \\(\\overrightarrow{a}\\) is in the same direction as \\(\\overrightarrow{b}\\), then \\(\\overrightarrow{a} > \\overrightarrow{b}\\).\"\n\nThis statement involves comparing magnitudes of... | [
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{
"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 any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following propositions is correct?\n\nA: If $|\\overrightarrow{a}| > |\\overrightarrow{b}|$ and $\\overrightarrow{a}$ is in the same direction as $\\overrightarrow{b}$, then $\\overrightarrow{a} > \\overrightarrow{b}$.\n\nB: $|\\overrightarrow{a} + \\overrightarrow{b}| \\leq |\\overrightarrow{a}| + |\\overrightarrow{b}|$\n\nC: If $\\overrightarrow{a} \\parallel \\overrightarrow{c}$, then there exists a unique real number $k$ such that $\\overrightarrow{a} = k\\overrightarrow{c}$.\n\nD: $|\\overrightarrow{a} - \\overrightarrow{b}| \\leq |\\overrightarrow{a}| - |\\overrightarrow{b}|$",
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[
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"value": "The condition \"a > 0, and a ≠ 1\" is the ( ) condition for \"loga2 > 0\".\nA: Sufficient but not necessary condition\nB: Necessary but not sufficient condition\nC: Sufficient and necessary condition\nD: Neither sufficient nor necessary condition"
},
{
"from": "assistant"... | The condition "a > 0, and a ≠ 1" is the ( ) condition for "loga2 > 0".
A: Sufficient but not necessary condition
B: Necessary but not sufficient condition
C: Sufficient and necessary condition
D: Neither sufficient nor necessary condition | 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"
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{
"content": "The condition \"a > 0, and a ≠ ... | B | original | [
"To determine whether the condition \\(a > 0\\) and \\(a \\neq 1\\) is sufficient, necessary, or both for the inequality \\(\\log_a 2 > 0\\), we need to analyze the properties of logarithms.\n\n### Step-by-Step Analysis:\n\n1. **Understanding the Inequality**:\n - The expression \\(\\log_a 2 > 0\\) means that the... | [
false,
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"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 condition \"a > 0, and a ≠ 1\" is the ( ) condition for \"loga2 > 0\".\nA: Sufficient but not necessary condition\nB: Necessary but not sufficient condition\nC: Sufficient and necessary condition\nD: Neither sufficient nor necessary condition",
"role": "user"
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[
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"value": "In a group of 2017 persons, any pair of persons has exactly one common friend (other than the pair of persons). Determine the smallest possible value of the difference between the numbers of friends of the person with the most friends and the person with the least friends in such... | In a group of 2017 persons, any pair of persons has exactly one common friend (other than the pair of persons). Determine the smallest possible value of the difference between the numbers of friends of the person with the most friends and the person with the least friends in such a group. | 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 group of 2017 persons, any... | 2014 | original | [
"To solve this problem, we need to understand the structure of the friendship graph described. Let's denote the group of people as vertices in a graph \\( G \\) where each edge represents a friendship.\n\nGiven that any two people have exactly one common friend, let's consider the implications for the graph:\n- Eac... | [
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"",
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"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 group of 2017 persons, any pair of persons has exactly one common friend (other than the pair of persons). Determine the smallest possible value of the difference between the numbers of friends of the person with the most friends and the person with the least friends in such a group.",
"role": "user"
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} | {
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"value": "Selene buys two instant cameras at $110 and three digital photo frames at $120 each. She gets a 5% discount on all the items she purchased. How much does she pay in all?"
},
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"value": "<think>\nOkay, so Selene bought two instant cameras and three... | null | tiger_math | 11,673 | [
{
"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": "Selene buys two instant cameras... | 551 | original | [
"First, we calculate the total cost of the instant cameras:\n- Cost per instant camera: $110\n- Number of instant cameras: 2\n\nTotal cost for instant cameras = \\( 110 \\times 2 = 220 \\)\n\nNext, we calculate the total cost of the digital photo frames:\n- Cost per digital photo frame: $120\n- Number of digital ph... | [
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"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": "Selene buys two instant cameras at $110 and three digital photo frames at $120 each. She gets a 5% discount on all the items she purchased. How much does she pay in all?",
"role": "user"
}
]
} | {
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[
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"value": "Given the preliminary coordinates of points Q, R, S, and T, along with their latitude and departure errors, compute the corrected coordinates for point T using the corrections derived from the Compass Rule. The preliminary coordinates are:\n\n- Q: (2600.480, 1391.670)\n- R: (2379... | null | automath | 32,975 | [
{
"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 preliminary coordinat... | (2713.905, 1727.185) | original | [
"To find the corrected coordinates of point T, we will use the corrections derived from the Compass Rule.\n\nFirstly, let's understand the error components:\n- Laterr_T = +0.555'\n- Deperr_T = -0.070'\n\nThese errors need to be applied to the coordinates of point T.\n\nThe formulae for correcting the coordinates ba... | [
false,
false
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"",
""
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{
"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 preliminary coordinates of points Q, R, S, and T, along with their latitude and departure errors, compute the corrected coordinates for point T using the corrections derived from the Compass Rule. The preliminary coordinates are:\n\n- Q: (2600.480, 1391.670)\n- R: (2379.780, 1723.774)\n- S: (2272.433, 1314.736)\n- T: (2713.835, 1727.740)\n\nThe respective latitude and departure errors during the traverse were found to be:\n\n- \\( \\text{Lat err}_T = 2713.835' - 2713.780' = +0.555' \\)\n- \\( \\text{Dep err}_T = 1727.740' - 1727.810' = -0.070' \\)\n\nWhat are the corrected coordinates of point T after applying the necessary corrections?",
"role": "user"
}
]
} | {
"backend": "litellm",
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[
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"value": "Find all functions $f:\\mathbb{R}\\rightarrow \\mathbb{R}$ such that\n$\\forall x\\in \\mathbb{R} \\ \\ f(x) = max(2xy-f(y))$ where $y\\in \\mathbb{R}$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find all functions \\( f: \\mathbb{R} \\rightarrow... | Find all functions $f:\mathbb{R}\rightarrow \mathbb{R}$ such that
$\forall x\in \mathbb{R} \ \ f(x) = max(2xy-f(y))$ where $y\in \mathbb{R}$. | 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": "Find all functions $f:\\mathbb{... | x^2 | original | [
"To find the function \\( f: \\mathbb{R} \\to \\mathbb{R} \\) satisfying the given functional equation, we start with:\n\n\\[ f(x) = \\max_{y \\in \\mathbb{R}} (2xy - f(y)). \\]\n\nFirstly, let's denote:\n\\[ g(x, y) = 2xy - f(y). \\]\nThen our original condition becomes:\n\\[ f(x) = \\max_{y \\in \\mathbb{R}} g(x,... | [
false,
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"",
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"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": "Find all functions $f:\\mathbb{R}\\rightarrow \\mathbb{R}$ such that\n$\\forall x\\in \\mathbb{R} \\ \\ f(x) = max(2xy-f(y))$ where $y\\in \\mathbb{R}$.",
"role": "user"
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[
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"value": "Return your final response within \\boxed{}. Alex wrote all natural divisors of a natural number \\( n \\) on the board in ascending order. Dima erased several of the first and several of the last numbers of the resulting sequence so that 151 numbers remained. What is the maximum... | Alex wrote all natural divisors of a natural number \( n \) on the board in ascending order. Dima erased several of the first and several of the last numbers of the resulting sequence so that 151 numbers remained. What is the maximum number of these 151 divisors that could be fifth powers of natural numbers? | 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... | 31 | original | [
"To determine the maximum number of divisors of \\( n \\) that are fifth powers, we need to analyze the structure of the divisors of \\( n \\). A divisor of \\( n \\) can be expressed as \\( d = p_1^{e_1} p_2^{e_2} \\cdots p_k^{e_k} \\), where \\( p_i \\) are prime factors of \\( n \\) and \\( e_i \\) are non-negat... | [
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{
"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 within <answer>...</answer>. Alex wrote all natural divisors of a natural number \\( n \\) on the board in ascending order. Dima erased several of the first and several of the last numbers of the resulting sequence so that 151 numbers remained. What is the maximum number of these 151 divisors that could be fifth powers of natural numbers?",
"role": "user"
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]
} | {
"backend": "litellm",
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"",
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[{"from":"user","value":"12. 10 consecutive natural numbers are arranged in ascending order. If the (...TRUNCATED) | "12. 10 consecutive natural numbers are arranged in ascending order. If the sum of the last 6 number(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | 6 | original | ["Let's denote the 10 consecutive natural numbers as \\( n, n+1, n+2, \\ldots, n+9 \\).\n\nFirst, we(...TRUNCATED) | [
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"",
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