2014-10-13 09:00:22

If a and b are integers, and if 3a + 4b = 17, which of the following could be the value of a?

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

The correct answer is D
Explanation: Plug in the answer choices for a and solve for b. If the resulting b is an integer, then the answer is correct. If it isn't, then it's not, since the prompt makes clear that a and b are both integers.

(A) a = 0: 3(o) + 4b = 17 means 4b = 17. That would make b = 17/4, not an integer.
(B) a = 1: 3(1) + 4b = 17 means 3 + 4b = 17. That would make 4b = 14 and b = 7/2, not an integer.
(C) a = 2: 3(2) + 4b = 17 means 6 + 4b = 17. That would make 4b = 11 and b = 11/4, not an integer.
(D) a = 3: 3(3) + 4b = 17 means 9 + 4b = 17. That would make 4b = 8 and b = 2. This is an integer!
(E) a = 4: 3(4) + 4b = 17 means 12 + 4b = 17. That would make 4b = 5 and b = 5/4, not an integer.

As only choice D results in both a and b being integers, choice D is correct, and a = 3 and b = 2.