2014-09-29 09:00:50

x and y are both positive integers such that x < y. If xy ≥ 12 and x + y ≤ 7, what is one possible value of y?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

The correct answer is B
Explanation: The fastest way to do this question is to plug in the answer choices, starting with the addition problem first. Since y has to be greater than x, start with the largest suggested value of y, and work down:

If y is 7, then x is 0 at most. This is impossible, because both x and y are supposed to be positive integers.

If y is 6, then x is 1 at most. However, 6 • 1 is 6, which is not greater than or equal to 12.

If y is 5, then x is 2 at most. However, 5 • 2 is 10, which is not greater than or equal to 12.

If y is 4, then x is 3 at most. 4 • 3 is 12, so choice B is correct: x is 3 and y is 4.