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If a and b are positive integers, is the product ab odd?

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by BTGmoderatorDC » Sun Sep 15, 2019 6:16 pm

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If a and b are positive integers, is the product ab odd?

(1) b = 3
(2) a and b are consecutive integers.

OA B

Source: Princeton Review
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Sun Sep 15, 2019 8:41 pm
BTGmoderatorDC wrote:If a and b are positive integers, is the product ab odd?

(1) b = 3
(2) a and b are consecutive integers.

OA B

Source: Princeton Review
Given a and b are positive integers, for the product ab to be odd, a as well as b must be odd. Even if only one of the two is even, the product ab is odd.

Let's take each statement one by one.

(1) b = 3

Even a is even, ab is even; however, if a is odd, the product is odd. Insufficient.

(2) a and b are consecutive integers.

Given that a and b are consecutive integers, one between a and b would be even and the other would be odd; thus, the product ab = even. The answer is no. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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