subset large_string | id int64 | query large_string | answer large_string | GT int64 | pred int64 | correct int64 | original_answer large_string | gen_answer large_string | correct_parsed int64 |
|---|---|---|---|---|---|---|---|---|---|
AIME2025-I | 0 | Solve the following AIME problem.
Give ONLY the final answer as an integer from 0 to 999.
Problem:
Find the sum of all integer bases $b>9$ for which $17_{b}$ is a divisor of $97_{b}$.
Final Answer: | <think>
Okay, so I need to solve this AIME problem where I have to find the sum of all integer bases b > 9 for which 17 base b divides 97 base b. Hmm, let me think about how to approach this.
First, I remember that numbers in different bases can be converted to base 10 to make them easier to work with. So, let me star... | 70 | 70 | 1 | <think>
Okay, so I need to solve this AIME problem where I have to find the sum of all integer bases b > 9 for which 17 base b divides 97 base b. Hmm, let me think about how to approach this.
First, I remember that numbers in different bases can be converted to base 10 to make them easier to work with. So, let me star... | 70 | 1 |
AIME2025-I | 1 | Solve the following AIME problem.
Give ONLY the final answer as an integer from 0 to 999.
Problem:
On $\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M... | <think>
Okay, so I need to solve this AIME problem. Let me try to visualize the problem first. There's a triangle ABC. On side AB, there are points A, D, E, B in that order, with AD = 4, DE = 16, and EB = 8. On side AC, there are points A, F, G, C in order, with AF = 13, FG = 52, and GC = 26. Then, M is the reflection ... | 588 | 588 | 1 | <think>
Okay, so I need to solve this AIME problem. Let me try to visualize the problem first. There's a triangle ABC. On side AB, there are points A, D, E, B in that order, with AD = 4, DE = 16, and EB = 8. On side AC, there are points A, F, G, C in order, with AF = 13, FG = 52, and GC = 26. Then, M is the reflection ... | 588 | 1 |
AIME2025-I | 2 | Solve the following AIME problem.
Give ONLY the final answer as an integer from 0 to 999.
Problem:
The 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of p... | <think>
Okay, so I need to solve this AIME problem about the baseball team going to an ice cream parlor. Let me try to understand the problem first.
We have 9 players, each choosing one of three flavors: chocolate, vanilla, or strawberry. The conditions are:
1. At least one player chose each flavor.
2. The number of ... | 16 | 16 | 1 | <think>
Okay, so I need to solve this AIME problem about the baseball team going to an ice cream parlor. Let me try to understand the problem first.
We have 9 players, each choosing one of three flavors: chocolate, vanilla, or strawberry. The conditions are:
1. At least one player chose each flavor.
2. The number of ... | 16 | 1 |
AIME2025-I | 3 | Solve the following AIME problem.
Give ONLY the final answer as an integer from 0 to 999.
Problem:
Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.
Final Answer: | <think>
Okay, so I need to solve this AIME problem where I have to find the number of ordered pairs (x, y) with both x and y integers between -100 and 100 inclusive, such that 12x² - xy - 6y² = 0. Hmm, let me think about how to approach this.
First, the equation is 12x² - xy - 6y² = 0. Maybe I can factor this equation... | 117 | 3 | 0 | <think>
Okay, so I need to solve this AIME problem where I have to find the number of ordered pairs (x, y) with both x and y integers between -100 and 100 inclusive, such that 12x² - xy - 6y² = 0. Hmm, let me think about how to approach this.
First, the equation is 12x² - xy - 6y² = 0. Maybe I can factor this equation... | 117 | 1 |
AIME2025-I | 4 | "Solve the following AIME problem.\nGive ONLY the final answer as an integer from 0 to 999.\n\nProbl(...TRUNCATED) | "<think>\nOkay, so I need to solve this AIME problem where I have to find the number of eight-digit (...TRUNCATED) | 279 | 6 | 0 | "<think>\nOkay, so I need to solve this AIME problem where I have to find the number of eight-digit (...TRUNCATED) | 504 | 0 |
AIME2025-I | 5 | "Solve the following AIME problem.\nGive ONLY the final answer as an integer from 0 to 999.\n\nProbl(...TRUNCATED) | "<think>\nOkay, so I need to solve this AIME problem about an isosceles trapezoid with an inscribed (...TRUNCATED) | 504 | 504 | 1 | "<think>\nOkay, so I need to solve this AIME problem about an isosceles trapezoid with an inscribed (...TRUNCATED) | 504 | 1 |
AIME2025-I | 6 | "Solve the following AIME problem.\nGive ONLY the final answer as an integer from 0 to 999.\n\nProbl(...TRUNCATED) | "<think>\nOkay, so I need to solve this AIME problem. Let me read it again carefully.\n\nWe have twe(...TRUNCATED) | 821 | 4 | 0 | "<think>\nOkay, so I need to solve this AIME problem. Let me read it again carefully.\n\nWe have twe(...TRUNCATED) | 7 | 0 |
AIME2025-I | 7 | "Solve the following AIME problem.\nGive ONLY the final answer as an integer from 0 to 999.\n\nProbl(...TRUNCATED) | "<think>\nOkay, so I need to solve this AIME problem. Let me read it again carefully.\n\nThe problem(...TRUNCATED) | 77 | 77 | 1 | "<think>\nOkay, so I need to solve this AIME problem. Let me read it again carefully.\n\nThe problem(...TRUNCATED) | 77 | 1 |
AIME2025-I | 8 | "Solve the following AIME problem.\nGive ONLY the final answer as an integer from 0 to 999.\n\nProbl(...TRUNCATED) | "<think>\nOkay, so I need to solve this AIME problem where a parabola y = x² - 4 is rotated 60 degr(...TRUNCATED) | 62 | 12 | 0 | "<think>\nOkay, so I need to solve this AIME problem where a parabola y = x² - 4 is rotated 60 degr(...TRUNCATED) | 49 | 0 |
AIME2025-I | 9 | "Solve the following AIME problem.\nGive ONLY the final answer as an integer from 0 to 999.\n\nProbl(...TRUNCATED) | "<think>\nOkay, so I need to solve this AIME problem about a 3x9 grid filled with numbers 1 through (...TRUNCATED) | 81 | 9 | 0 | "<think>\nOkay, so I need to solve this AIME problem about a 3x9 grid filled with numbers 1 through (...TRUNCATED) | 216 | 0 |
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