Edition 3

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

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