Data Sufficiency

lheiannie07 wrote:If a and b are integers, and m is an even integer, is ab/4 an integer?

(1) a+b is even.
(2) m/(ab) is an odd integer.

Statement 1:
Case 1: a=1 and b=1, with the result that a+b = 1+1 = 2
In this case, ab/4 = (1*1)/4 = 1/4, so the answer to the question stem is NO.
Case 2: a=2 and b=2, with the result that a+b = 2+2 = 4
In this case, ab/4 = (2*2)/4 = 4/4 = 1, so the answer to the question stem is YES.
INSUFFICIENT.

Statement 2:
Since m is even, we get:
even/(ab) = odd
even = (odd)(ab)
ab = even/odd
ab = even.

Case 2 (a=2 and b=2) also satisfies Statement 2, since ab = 2*2 = 4, with the result that ab = even.
In Case 2, the answer to the question stem is YES.
Case 3: a=1 and b=2, with the result that ab = 1*2 = 2
In this case, ab/4 = (1*2)/4 = 1/2, so the answer to the question stem is NO.
INSUFFICIENT.

Statements combined:
a+b = even and ab=even are possible only if a and b are both EVEN.
The product of two even numbers will always be a MULTIPLE OF 4.
Thus, ab/4 = (multiple of 4)/4 = integer.
The answer to the question stem is YES.
SUFFICIENT.

The correct answer is C.

An algebraic proof for the statements combined:
Since a and b are both even, they can be represented as follows:
a = 2x and b = 2y, with the result that ab = (2x)(2y) = 4xy.
Thus:
ab/4 = (4xy)/4 = xy = integer.