| 2461 |
AIME 2021 II Q10 |
Two spheres with radii \(36\) and one sphere with ... |
1500.00 |
| 2462 |
AIME 2021 II Q13 |
Find the least positive integer \(n\) for which \(... |
1500.00 |
| 2463 |
AIME 2021 II Q14 |
Let \(\triangle ABC\) be an acute triangle with ci... |
1500.00 |
| 2464 |
AIME 2021 II Q15 |
Let \(f(n)\) and \(g(n)\) be functions satisfying
... |
1500.00 |
| 2465 |
AIME 1991 I Q1 |
Find \(x^2+y^2\) if \(x\) and \(y\) are positive i... |
1500.00 |
| 2466 |
AIME 1991 I Q4 |
How many real numbers \(x\) satisfy the equation \... |
1500.00 |
| 2467 |
AIME 1991 I Q5 |
Given a rational number, write it as a fraction in... |
1500.00 |
| 2468 |
AIME 1991 I Q6 |
Suppose \(r\) is a real number for which \[ \left\... |
1500.00 |
| 2469 |
AIME 1991 I Q8 |
For how many real numbers \(a\) does the quadratic... |
1500.00 |
| 2470 |
AIME 1991 I Q9 |
Suppose that \(\sec x+\tan x=\frac{22}7\) and that... |
1500.00 |
| 2471 |
AIME 1991 I Q10 |
Two three-letter strings, \(aaa\) and \(bbb\), are... |
1500.00 |
| 2472 |
AIME 1991 I Q11 |
Twelve congruent disks are placed on a circle \(C\... |
1500.00 |
| 2473 |
AIME 1991 I Q12 |
Rhombus \(PQRS\) is inscribed in rectangle \(ABCD\... |
1500.00 |
| 2474 |
AIME 1991 I Q13 |
A drawer contains a mixture of red socks and blue ... |
1500.00 |
| 2475 |
AIME 1991 I Q14 |
A hexagon is inscribed in a circle. Five of the si... |
1500.00 |
| 2476 |
AIME 1991 I Q15 |
For positive integer \(n\), define \(S_n\) to be t... |
1500.00 |
| 2477 |
AIME 2010 I Q1 |
Maya lists all the positive divisors of \( 2010^2\... |
1500.00 |
| 2478 |
AIME 2010 I Q3 |
Suppose that \( y = \frac34x\) and \( x^y = y^x\).... |
1500.00 |
| 2479 |
AIME 2010 I Q4 |
Jackie and Phil have two fair coins and a third co... |
1500.00 |
| 2480 |
AIME 2010 I Q6 |
Let \( P(x)\) be a quadratic polynomial with real ... |
1500.00 |