BTGmoderatorDC wrote: ↑Wed May 06, 2020 6:40 pm
If c and d are integers, is c even?
(1) c(d + 1) is even
(2) (c + 2)(d + 4) is even
OA
C
Source: GMAT Prep
Let's take each statement one by one.
(1) c(d + 1) is even.
Case 1: Say c is even and d is even/odd, then c(d + 1) is even. The answer is yes.
Case 2: Say c is odd and d is odd, then c(d + 1) is even. The answer is no.
No unique answer. Insufficient.
(2) (c + 2)(d + 4) is even.
Case 1: Say c is even and d is even/odd, then (c + 2)(d + 4) is even. The answer is yes.
Case 2: Say c is odd and d is even, then (c + 2)(d + 4) is even. The answer is no.
No unique answer. Insufficient.
(1) and (2) together
From Case 2 of each statement, we get that c cannot be odd since in Case 2 of Statement 1, we have d is odd, whereas in Case 2 of Statement 2, we have d is even, which is not possible, Thus, c is even. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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