BTGmoderatorDC wrote:Is b even?
(1) a/b is even
(2) (a+1)b is even
OA E
Source: Veritas Prep
Let's take each statement one by one.
(1) a/b is even.
Note that Even/Even and Even by Odd can be even.
Case 1: Say a = 4 and b = 2 (even), then a/b = 4/2 = 2 (even); the answer is Yes.
Case 2: Say a = 6 and b = 3 (odd), then a/b = 6/3 = 2 (even); the answer is No.
No unique answer. Insufficient.
(2) (a+1)b is even.
Note that for the product of two numbers to be even, at least one of the numbers need to be even. So, in this case, if b is even, the answer is Yes; however, if b is odd and (a + 1) is even or a is odd, the answer is No.
No unique answer. Insufficient.
(1) and (2) together
Note that we must not assume that a and b are integers.
Case 1: Say a = 4 and b = 2 (even), then a/b = 4/2 = 2 (even) and (a+1)b = (4 + 1)*2 = 10 (even); the answer is Yes.
Case 2: Say a = 3 and b = 0.5 (not even), then a/b = 3/0.5 = 6 (even) and (a+1)b = (3 + 1)*0.5 = 4*0.5 = 2 (even); the answer is No.
No unique answer. Insufficient.
The correct answer:
E
Hope this helps!
-Jay
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