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If a and b are integers and ab

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by BTGmoderatorDC » Tue Mar 10, 2020 6:32 pm

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C

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E

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Difficulty—

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
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Re: If a and b are integers and ab

by Jay@ManhattanReview » Tue Mar 10, 2020 9:45 pm
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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Re: If a and b are integers and ab

by Scott@TargetTestPrep » Sat Mar 14, 2020 9:52 am
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
We can simplify the given expression:

a(b - 1) = odd

Since odd x odd = odd, we see that a has to be odd and (b - 1) has to be odd, which means b must be even.

Since even + odd (or odd + even) = odd, we see that a^2 + b must be odd:

a^2 = odd^2 = odd number

b = even number

Thus, odd + even = odd.

Answer: C

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