instruction_seed stringlengths 18 5.45k | response_seed stringlengths 18 5.45k | reasoning stringlengths 1.07k 91.6k | deepseek_solution stringlengths 299 2.58k | __original_row_idx int64 11 40k | source stringclasses 1
value | final_reasoning_trace stringlengths 1.56k 93.2k | conversations listlengths 2 2 |
|---|---|---|---|---|---|---|---|
What is the maximum possible value for $z$ in the equation $z = 3x^2 - 8x - 10$? | What is the maximum possible value for $z$ in the equation $z = 3x^2 - 8x - 10$? | Okay, so I need to find the maximum possible value for z in the equation z = 3x² - 8x - 10. Hmm, let me think. I remember that quadratic equations graph as parabolas. Since the coefficient of x² here is 3, which is positive, that means the parabola opens upwards. Wait, if it opens upwards, then the vertex would be the ... | To find the maximum possible value for \( z \) in the equation \( z = 3x^2 - 8x - 10 \), we first recognize that this is a quadratic equation. The coefficient of \( x^2 \) is 3, which is positive, indicating that the parabola opens upwards.
Since the parabola opens upwards, it has a minimum value at its vertex and no... | 25,122 | ai2-adapt-dev/openmath-2-math | <think>
Okay, so I need to find the maximum possible value for z in the equation z = 3x² - 8x - 10. Hmm, let me think. I remember that quadratic equations graph as parabolas. Since the coefficient of x² here is 3, which is positive, that means the parabola opens upwards. Wait, if it opens upwards, then the vertex would... | [
{
"from": "human",
"value": "What is the maximum possible value for $z$ in the equation $z = 3x^2 - 8x - 10$?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the maximum possible value for z in the equation z = 3x² - 8x - 10. Hmm, let me think. I remember that quadratic equations... |
Find the least multiple of 7 that has exactly 12 positive divisors. | Find the least multiple of 7 that has exactly 12 positive divisors. | Okay, so I need to find the smallest multiple of 7 that has exactly 12 positive divisors. Hmm, let's break this down. First, multiples of 7 are numbers like 7, 14, 21, 28, and so on. Each is 7 multiplied by an integer starting from 1. Now, the task is to find the least such multiple where the number of divisors is exac... | To find the least multiple of 7 that has exactly 12 positive divisors, we start by noting that the number of divisors of a number \( N \) with prime factorization \( N = p_1^{a_1} \cdot p_2^{a_2} \cdot \ldots \cdot p_n^{a_n} \) is given by \( (a_1 + 1)(a_2 + 1) \cdots (a_n + 1) \). We need this product to be 12 and the... | 15,638 | ai2-adapt-dev/openmath-2-math | <think>
Okay, so I need to find the smallest multiple of 7 that has exactly 12 positive divisors. Hmm, let's break this down. First, multiples of 7 are numbers like 7, 14, 21, 28, and so on. Each is 7 multiplied by an integer starting from 1. Now, the task is to find the least such multiple where the number of divisors... | [
{
"from": "human",
"value": "Find the least multiple of 7 that has exactly 12 positive divisors."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the smallest multiple of 7 that has exactly 12 positive divisors. Hmm, let's break this down. First, multiples of 7 are numbers like 7,... |
"Let $g$ be a function mapping the set of positive integers to the set of positive integers, such th(...TRUNCATED) | "Let $g$ be a function mapping the set of positive integers to the set of positive integers, such th(...TRUNCATED) | "Okay, let's try to figure out what the function g is. The problem says that g is an increasing func(...TRUNCATED) | "Given the function \\( g \\) mapping the set of positive integers to the set of positive integers w(...TRUNCATED) | 21,051 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, let's try to figure out what the function g is. The problem says that g is an increa(...TRUNCATED) | [{"from":"human","value":"Let $g$ be a function mapping the set of positive integers to the set of p(...TRUNCATED) |
"Consider the binary operation defined by $(a \\bullet b) = \\frac{a}{b}$. Find the value of $(3 \\b(...TRUNCATED) | "Consider the binary operation defined by $(a \\bullet b) = \\frac{a}{b}$. Find the value of $(3 \\b(...TRUNCATED) | "Okay, so I have this problem here: Consider the binary operation defined by (a • b) = a/b. Find t(...TRUNCATED) | "To solve the problem, we need to evaluate the expression \\((3 \\bullet 4) \\bullet (2 \\bullet 6)\(...TRUNCATED) | 5,860 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I have this problem here: Consider the binary operation defined by (a • b) = a/(...TRUNCATED) | [{"from":"human","value":"Consider the binary operation defined by $(a \\bullet b) = \\frac{a}{b}$. (...TRUNCATED) |
Subtract $111.11$ from $333.33.$ Express the result as a decimal to the nearest hundredth. | Subtract $111.11$ from $333.33.$ Express the result as a decimal to the nearest hundredth. | "Okay, so I need to subtract 111.11 from 333.33 and then make sure the result is a decimal rounded t(...TRUNCATED) | "To subtract \\(111.11\\) from \\(333.33\\), we start by aligning the numbers by their decimal point(...TRUNCATED) | 28,290 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I need to subtract 111.11 from 333.33 and then make sure the result is a decimal (...TRUNCATED) | [{"from":"human","value":"Subtract $111.11$ from $333.33.$ Express the result as a decimal to the ne(...TRUNCATED) |
"A cylindrical container has a height of 20 inches and a circular base with a diameter of 18 inches.(...TRUNCATED) | "A cylindrical container has a height of 20 inches and a circular base with a diameter of 18 inches.(...TRUNCATED) | "Alright, so I need to figure out the radius of the smallest spherical ornament that can fit complet(...TRUNCATED) | "The cylindrical container has a height of 20 inches and a circular base with a diameter of 18 inche(...TRUNCATED) | 7,449 | ai2-adapt-dev/openmath-2-math | "<think>\nAlright, so I need to figure out the radius of the smallest spherical ornament that can fi(...TRUNCATED) | [{"from":"human","value":"A cylindrical container has a height of 20 inches and a circular base with(...TRUNCATED) |
"Find the minimum value of $|x-y|$ given that $x$ and $y$ are positive integers satisfying the equat(...TRUNCATED) | "Find the minimum value of $|x-y|$ given that $x$ and $y$ are positive integers satisfying the equat(...TRUNCATED) | "Okay, so I need to find the minimum value of |x - y| where x and y are positive integers that satis(...TRUNCATED) | "Given the equation \\(xy + 2x - 5y = 221\\) where \\(x\\) and \\(y\\) are positive integers, we nee(...TRUNCATED) | 19,283 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I need to find the minimum value of |x - y| where x and y are positive integers t(...TRUNCATED) | [{"from":"human","value":"Find the minimum value of $|x-y|$ given that $x$ and $y$ are positive inte(...TRUNCATED) |
"George has a quadratic of the form $x^2+bx+\\frac13$, where $b$ is a specific negative number. Usin(...TRUNCATED) | "George has a quadratic of the form $x^2+bx+\\frac13$, where $b$ is a specific negative number. Usin(...TRUNCATED) | "Okay, so I need to figure out the value of \\( b \\) in the quadratic equation \\( x^2 + bx + \\fra(...TRUNCATED) | "George has a quadratic of the form \\( x^2 + bx + \\frac{1}{3} \\), where \\( b \\) is a specific n(...TRUNCATED) | 13,378 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I need to figure out the value of \\( b \\) in the quadratic equation \\( x^2 + b(...TRUNCATED) | [{"from":"human","value":"George has a quadratic of the form $x^2+bx+\\frac13$, where $b$ is a speci(...TRUNCATED) |
"In a village, there are 10 houses, and each house has a different color. Each day, each villager vi(...TRUNCATED) | "In a village, there are 10 houses, and each house has a different color. Each day, each villager vi(...TRUNCATED) | "Okay, so I need to figure out how many days the villagers can keep visiting houses under these rule(...TRUNCATED) | "Given 10 houses, each with a different color, each villager visits exactly 3 different houses each (...TRUNCATED) | 37,356 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I need to figure out how many days the villagers can keep visiting houses under t(...TRUNCATED) | [{"from":"human","value":"In a village, there are 10 houses, and each house has a different color. E(...TRUNCATED) |
"Find the product of the roots of the equation $x^4 - 2x^3 + 5x^2 - x - 1 = 0$. Express your answer (...TRUNCATED) | "Find the product of the roots of the equation $x^4 - 2x^3 + 5x^2 - x - 1 = 0$. Express your answer (...TRUNCATED) | "Okay, so I need to find the product of the roots of the equation \\( x^4 - 2x^3 + 5x^2 - x - 1 = 0 (...TRUNCATED) | "To find the product of the roots of the equation \\(x^4 - 2x^3 + 5x^2 - x - 1 = 0\\), we use Vieta'(...TRUNCATED) | 20,510 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I need to find the product of the roots of the equation \\( x^4 - 2x^3 + 5x^2 - x(...TRUNCATED) | [{"from":"human","value":"Find the product of the roots of the equation $x^4 - 2x^3 + 5x^2 - x - 1 =(...TRUNCATED) |
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