If c - ab is an odd integer, where a, b and c are integers, is a odd?

Question

(1) ab + ac is even
(2) b + ab is even

gmatophobia · Answer

We can find the conditions in which c - ab is an odd integer. Once the conditions are found each statement can be individually evaluated.

Statement 1

(1) ab + ac is even

a (b + c) = even

Case 1  a = even

Case 2  a = odd AND (b+c) = even

If (b+c) = even, either b and c both are even or both b and c are odd.

However, the case 2 will not hold true, as the combination violates the base condition , c - ab = odd.

Hence statement 1 is sufficient.

Statement 2

(2) b + ab is even

No information on c. Additionally, when b is even c can be even or odd.

Option A

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