BTGmoderatorDC wrote: ↑Tue Mar 10, 2020 6:32 pm
If a and b are integers and ab − a is odd, which of the following must be odd?
(A) b^2
(B) b
(C) a^2 + b
(D) ab
(E) ab + b
OA
C
Source: Veritas Prep
Let's write ab – b as a(b – 1). Since a(b – 1) is odd, it is possible if a and (b – 1) both are odd. Now since (b – 1) is odd, we have b even.
So, finally, we have a an odd integer and b an even integer. Let's see each option one by one.
(A) b^2: Even^2 = Even
(B) b: Already know that b is even.
(C) a^2 + b: Even^2 + Odd = Even + Odd = Odd. The correct answer.
(D) ab: Even*Odd = Even
(E) ab + b: Even*Odd +Even = Even + Even = Even
The correct answer:
C
Hope this helps!
-Jay
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