Problem #23-Solved by Peter Dun

A club has $10$ members, $5$ boys and $5$ girls. Two of the members are chosen at random. What is the probability that they are both girls?

Problem #22-Solved by Peter Dun

A small car company operates machinery for $t$ hours per day that produces $c$ cars per hour, where $c$ and $t$ are positive integers. After upgrading the machinery, the company can now produce$2c+5$ cars per hour. If the machinery now operates for $t-2$ hours per day and yet produces the same number of cars per day, how many cars per day does it produce?

Problem #21-Solved by Peter Dun

Find the sum of all whole numbers $x$ that satisfy $x+\frac{25}{x}=10$.

Problem #20-Solved by function

Find the largest integer $n$ such that $n$ has exactly $4$ positive divisors and $n$ divides $100!$.

Problem #19-Solved by Peter Dun

If the diagonal of a cube is $5$, what is the volume of the cube? Express your answer in simplest radical form.

Problem #18-Solved by Peter Dun

Find a $3$-digit palindrome where the square of the product of the digits equals the sum of the digits.

Problem #17-Solved by Peter Dun

What is the area of the region defined by $|x-12|+|2y+5|\le7$?

Problem #16-Solved by function

Parabola needs to catch a train. The train arrives randomly some time between 1:00 and 2:00, waits for $10$ minutes, and then leaves. If Parabola also arrives randomly between 1:00 and 2:00, what is the probability that the train will be there when Parabola arrives?


This problem is extra hard, so the correct answer gets $20$ PP.

Problem #15-Solved by Peter Dun

What is the least number that has a remainder of $1$ when divided by the first $8$ positive integers?

Problem #14-Solved by function

If an integer greater than $1$ raised to the $\frac{1}{2}$, $\frac{1}{3}$, and $\frac{1}{4}$ power remains an integer, what is the least possible integer that satisfies these conditions?