Bunuel wrote:
The expression ab+a is odd when the a and b are integers. Which of the following expressions must be even?
(A) a
(B) b
(C) a + b
(D) ab - a
(E) a + b²
GIVEN: ab+a is odd
Factor to get: a(b+1) is ODD
This means a and b+1 must be ODD, which means b must be EVEN
So, we already know that
a is odd and
b is evenSo, a quick approach will be to take each answer choice and replace a with
1 (odd) and replace b with
0 (even)
We get:
(A)
1 = ODD (ELIMINATE)
(B)
0 = EVEN. keep
(C)
1 +
0 = 1, which is ODD (ELIMINATE)
(D) (
1)(
0) -
1 = -1, which is ODD (ELIMINATE)
(E)
1 +
0² = 1, which is ODD (ELIMINATE)
Answer: B
Cheers,
Brent
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