instruction_seed stringlengths 15 5.67k | response_seed stringlengths 15 5.67k | reasoning stringlengths 1.28k 65.9k | deepseek_solution stringlengths 7 2.46k | __original_row_idx int64 3 40k | source stringclasses 1
value | final_reasoning_trace stringlengths 1.51k 67.5k | conversations listlengths 2 2 |
|---|---|---|---|---|---|---|---|
The ratio of measures of two complementary angles is 4 to 5. The smallest measure is increased by $10\%$. By what percent must the larger measure be decreased so that the two angles remain complementary? | The ratio of measures of two complementary angles is 4 to 5. The smallest measure is increased by $10\%$. By what percent must the larger measure be decreased so that the two angles remain complementary? | Okay, so I need to solve this problem about complementary angles. Let me read it again carefully. The ratio of the measures of two complementary angles is 4 to 5. The smallest measure is increased by 10%. By what percent must the larger measure be decreased so that the two angles remain complementary?
Alright, complem... | The ratio of the measures of two complementary angles is 4 to 5. Let the measures of the angles be \(4x\) and \(5x\). Since complementary angles add up to 90 degrees, we have:
\[
4x + 5x = 90 \implies 9x = 90 \implies x = 10
\]
Thus, the measures of the angles are \(40^\circ\) and \(50^\circ\).
The smallest angle (4... | 23,262 | ai2-adapt-dev/openmath-2-math | <think>
Okay, so I need to solve this problem about complementary angles. Let me read it again carefully. The ratio of the measures of two complementary angles is 4 to 5. The smallest measure is increased by 10%. By what percent must the larger measure be decreased so that the two angles remain complementary?
Alright,... | [
{
"from": "human",
"value": "The ratio of measures of two complementary angles is 4 to 5. The smallest measure is increased by $10\\%$. By what percent must the larger measure be decreased so that the two angles remain complementary?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to sol... |
A five-digit number is divisible by 9. If the sum of the first three digits is equal to the sum of the last two digits, find the remainder when the square of the number is divided by 9. | A five-digit number is divisible by 9. If the sum of the first three digits is equal to the sum of the last two digits, find the remainder when the square of the number is divided by 9. | Okay, let's tackle this problem step by step. So, we have a five-digit number that's divisible by 9. The condition given is that the sum of the first three digits is equal to the sum of the last two digits. We need to find the remainder when the square of this number is divided by 9. Alright, let's start breaking this ... | Given a five-digit number divisible by 9, where the sum of the first three digits is equal to the sum of the last two digits, we need to find the remainder when the square of the number is divided by 9.
1. **Divisibility by 9**: A number is divisible by 9 if the sum of its digits is a multiple of 9. Let the five-digit... | 5,545 | ai2-adapt-dev/openmath-2-math | <think>
Okay, let's tackle this problem step by step. So, we have a five-digit number that's divisible by 9. The condition given is that the sum of the first three digits is equal to the sum of the last two digits. We need to find the remainder when the square of this number is divided by 9. Alright, let's start breaki... | [
{
"from": "human",
"value": "A five-digit number is divisible by 9. If the sum of the first three digits is equal to the sum of the last two digits, find the remainder when the square of the number is divided by 9."
},
{
"from": "gpt",
"value": "<think>\nOkay, let's tackle this problem step by s... |
"A rectangular prism with integer edge lengths is cut into eight non-overlapping cubes. The volume o(...TRUNCATED) | "A rectangular prism with integer edge lengths is cut into eight non-overlapping cubes. The volume o(...TRUNCATED) | "Alright, so I have this problem here about a rectangular prism with integer edge lengths that's bee(...TRUNCATED) | "Given a rectangular prism with integer edge lengths, volume 2160 cubic units, and divided into eigh(...TRUNCATED) | 33,554 | ai2-adapt-dev/openmath-2-math | "<think>\nAlright, so I have this problem here about a rectangular prism with integer edge lengths t(...TRUNCATED) | [{"from":"human","value":"A rectangular prism with integer edge lengths is cut into eight non-overla(...TRUNCATED) |
"In a regular tetrahedron, each edge measures 8 units. What is the total area, in square units, of t(...TRUNCATED) | "In a regular tetrahedron, each edge measures 8 units. What is the total area, in square units, of t(...TRUNCATED) | "Okay, so I need to find the total area of the four triangular faces of a regular tetrahedron where (...TRUNCATED) | "To find the total area of the four triangular faces of a regular tetrahedron with each edge measuri(...TRUNCATED) | 24,459 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I need to find the total area of the four triangular faces of a regular tetrahedr(...TRUNCATED) | [{"from":"human","value":"In a regular tetrahedron, each edge measures 8 units. What is the total ar(...TRUNCATED) |
"Find the sum of the coefficients in the polynomial $-2(x^7 - x^4 + 3x^2 - 5) + 4(x^3 + 2x) - 3(x^5 (...TRUNCATED) | "Find the sum of the coefficients in the polynomial $-2(x^7 - x^4 + 3x^2 - 5) + 4(x^3 + 2x) - 3(x^5 (...TRUNCATED) | "Okay, so I need to find the sum of the coefficients in this polynomial: -2(x⁷ - x⁴ + 3x² - 5) (...TRUNCATED) | "To find the sum of the coefficients in the polynomial \\(-2(x^7 - x^4 + 3x^2 - 5) + 4(x^3 + 2x) - 3(...TRUNCATED) | 18,855 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I need to find the sum of the coefficients in this polynomial: -2(x⁷ - x⁴ + 3(...TRUNCATED) | [{"from":"human","value":"Find the sum of the coefficients in the polynomial $-2(x^7 - x^4 + 3x^2 - (...TRUNCATED) |
"A certain organization has 18 members who each take turns serving as officers for 2 weeks at a time(...TRUNCATED) | "A certain organization has 18 members who each take turns serving as officers for 2 weeks at a time(...TRUNCATED) | "Okay, let me try to figure out this problem. So, there's an organization with 18 members, and each (...TRUNCATED) | "The organization originally has 18 members, but 6 leave, leaving 12 members. We need to find the nu(...TRUNCATED) | 16,037 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, let me try to figure out this problem. So, there's an organization with 18 members, (...TRUNCATED) | [{"from":"human","value":"A certain organization has 18 members who each take turns serving as offic(...TRUNCATED) |
"The hypotenuse of a right triangle whose legs are consecutive multiples of 3 is 40 units. What is t(...TRUNCATED) | "The hypotenuse of a right triangle whose legs are consecutive multiples of 3 is 40 units. What is t(...TRUNCATED) | "Okay, so I have this problem here: The hypotenuse of a right triangle whose legs are consecutive mu(...TRUNCATED) | "Given a right triangle with legs that are consecutive multiples of 3 and a hypotenuse of 40 units, (...TRUNCATED) | 38,501 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I have this problem here: The hypotenuse of a right triangle whose legs are conse(...TRUNCATED) | [{"from":"human","value":"The hypotenuse of a right triangle whose legs are consecutive multiples of(...TRUNCATED) |
"A prime number is called \"unusual\" if it is not divisible by the product of its digits. Find the (...TRUNCATED) | "A prime number is called \"unusual\" if it is not divisible by the product of its digits. Find the (...TRUNCATED) | "Okay, so I need to find the smallest unusual prime number. Let me start by understanding the proble(...TRUNCATED) | "To determine the smallest unusual prime number, we need to check each prime number in ascending ord(...TRUNCATED) | 7,063 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I need to find the smallest unusual prime number. Let me start by understanding t(...TRUNCATED) | [{"from":"human","value":"A prime number is called \"unusual\" if it is not divisible by the product(...TRUNCATED) |
"Six congruent copies of the parabola $y = x^2$ are arranged in the plane so that each vertex is tan(...TRUNCATED) | "Six congruent copies of the parabola $y = x^2$ are arranged in the plane so that each vertex is tan(...TRUNCATED) | "Alright, so I need to find the radius of the circle that's tangent to six congruent parabolas arran(...TRUNCATED) | "To find the radius of the circle tangent to six congruent copies of the parabola \\( y = x^2 \\) ar(...TRUNCATED) | 15,372 | ai2-adapt-dev/openmath-2-math | "<think>\nAlright, so I need to find the radius of the circle that's tangent to six congruent parabo(...TRUNCATED) | [{"from":"human","value":"Six congruent copies of the parabola $y = x^2$ are arranged in the plane s(...TRUNCATED) |
"Let $O$ be the origin. There exists a scalar $m$ so that for any points $P,$ $Q,$ $R,$ and $S$ suc(...TRUNCATED) | "Let $O$ be the origin. There exists a scalar $m$ so that for any points $P,$ $Q,$ $R,$ and $S$ suc(...TRUNCATED) | "Okay, so I need to find the scalar \\( m \\) such that for any points \\( P, Q, R, S \\) satisfying(...TRUNCATED) | "To find the scalar \\( m \\) such that for any points \\( P, Q, R, \\) and \\( S \\) satisfying the(...TRUNCATED) | 38,663 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I need to find the scalar \\( m \\) such that for any points \\( P, Q, R, S \\) s(...TRUNCATED) | [{"from":"human","value":"Let $O$ be the origin. There exists a scalar $m$ so that for any points $(...TRUNCATED) |
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