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For all integer values of a and b such that a > 0 and b<0, which of the following must also be an integer?

(F) 3a+b

(G) 3a-b

(H) 3ab

(J) 3-a


The Correct Answer

For all a ≠ 0 and b ≠ 0,

(A) (B) (C) (D) (E)

Correct Answer: D

Amy's best marathon time decreased by 10% from 2005 to 2006 and by 20% from 2006 to 2007. By what percent did her best marathon time decrease from 2005 to 2007?

(A)28% (B) 30% (C) 50% (D) 72% (E) 10%

Correct Answer: A

Rectangle ABCD lies in the standard (x,y) coordinate plane with corners at A(4,2), B(6,-1), C(1,-4), and D(-1,-1), and is represented by the 2 × 4 matrix . ABCD is then translated, with the corners of the translated rectangle represented by the matrix . What is the value of n?

(A) 0 (B) -1 (C) -2 (D) -3 (E) -4

Correct Answer: A

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