THE FACT THAT THE QUOTIENT C IS EVEN TELLS US THAT THE NUMERATOR A...

24. The fact that the quotient

c

is even tells us that the

numerator ab

²

is even.

If ab

²

were odd, the quotient would never be divisible by 2,

regardless of what c is. To prove this try to divide an odd number

by any integer to come up with an even number; you can't. If ab

²

is even, either a is even or b is even.

(I) TRUE: Since a or b is even, the product ab must be even

(II) NOT NECESSARILY: For the quotient to be positive, a and c

must have the same sign since b

²

is definitely positive. We know

nothing about the sign of b. The product of ab could be negative or

positive.

(III) NOT NECESSARILY: For the quotient to be even, ab

²

must be

even but c could be even or odd. An even number divided by an

odd number could be even (ex: 18/3), as could an even number

divided by an even number (ex: 16/4).

The correct answer is A.