1. A segment has endpoints P(1,1) and Q(x,y). The coordinates of the midpoint of segment PQ are positive integers with a product of 36. What is the maximum possible value of x?

2. Given that 591,3d8 is divisible by 12, what is the sum of all of the digits that could replace d?

3. The integer 6 has four positive divisors: 1, 2, 3 and 6. What is the smallest positivie integer with exactly five positive divisors?

4. What is the units digit of 2013^2013?

5. What is the sum of all of the two-digit primes that are greater than 12 but less than 99 and are still prime when their two digits are interchanged?

Guest Sep 15, 2022