BTGmoderatorDC wrote: ↑

Thu Feb 11, 2021 5:53 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

If \(a\) and \(b\) are integers and \(ab - a\) is odd.

Then \(a(b-1)\) is odd
Also, \(a\) and \((b-1)\) are odds
Therefore, \(b= (b-1)+1\) is even

So, we have
I) \(a\) odd
II) \(b\) even

Which of the following must be odd?

(A) \(b^2\) even\(^2 =\) even. NOT \(\Large{\color{red}\chi}\)
(B) \(b\) even. NOT \(\Large{\color{red}\chi}\)
(C) \(a^2 + b =\) odd\(^2 +\) even \(=\) odd \(+\) even \(=\) odd. YES \(\Large{\color{green}\checkmark}\)
(D) \(ab =\) odd \(\times\) even \(=\) even. NOT \(\Large{\color{red}\chi}\)
(E) \(ab + b\) odd \(\times\) even \(+\) even \(=\) even \(+\) even \(=\) even NOT. \(\Large{\color{red}\chi}\)