(12)
Adam and David are playing a game on a circular board with n spaces. Both players place their chip
at the same starting space. First Adam moves his chip forward five spaces from the starting space, then
David moves his chip forward seven, then Adam five, then David seven, and so on. The first player to
finish his turn on the starting space wins the game. If n is a random two-digit number, what is the
probability that Adam wins?
(A) (B) 7 (C) 3 (D) 3 (E) 43
(13)
Let ABC be a triangle such that AC = BC and ZACB = 80°. Let M be a point inside AABC such
that ZMBA = 30° and ZMAB = 10°. In degrees, find ZAMC.
(A) 50 (B) 65 (C) 68 (D) 70 (E) 75
(14)
Determine the number of integer numbers a for which the equation 23 – 13x + a = 0 has three integer
roots.
(A) O (B) 1 (C) 2 (D) 3 (E) 4
(15)
Let a1, A2, A3, ... be a sequence of positive real numbers such that akak+2 = Ak+1+1
for all positive integers k. If aj and a2 are both positive integers, find the maximum possible
value of a 2024
(A) 3
(B) 5
(C) 6
(D) 9
(E) 13
