1. Consider the 12 face diagonals of a rectangular block. How many pairs of them are skew lines?
(A) 30
(B) 60
(C) 24
(D) 48
(E) 72
2. How many finite arithmetic progressions of length at least 3 are there, with the first term and the common difference being positive integers, such that the sum of all the terms is 972?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
3. What is the number of pairs (x, y) of real numbers satisfying |tan πy| + sin2 πx = 0 and x2 + y2 ≤ 2?
(A) 4
(B) 5
(C) 8
(D) 9
(E) 10