If p and j are positive integers, is p + j even?

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BTGmoderatorLU: Moderator; Posts: 2550; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Mon Oct 23, 2017 3:39 pm

If p and j are positive integers, is p + j even?

(1) p - j is odd
(2) p = j + 1

The OA is D.

Can any expert explain this DS questios please? I don't have it clear. Thanks.

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Source: Beat The GMAT — Data Sufficiency | Mon Oct 23, 2017 3:39 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Wed Oct 25, 2017 1:17 am

LUANDATO wrote:If p and j are positive integers, is p + j even?

(1) p - j is odd
(2) p = j + 1

The OA is D.

Can any expert explain this DS questios please? I don't have it clear. Thanks.

(1) p - j is odd.

Since p - j = an odd integer, one of p and j is even and the other is odd. Both even or both odd will give an even integer.

Thus, p + j = sum of an even and an odd number = odd. The answer is No. Sufficient.

(2) p = j + 1

This implies that p and j are consecutive integers. One of the two consecutive integers would be even and the other would be odd.

Thus like Statement 1, p + j = sum of an even and an odd number = odd. The answer is No. Sufficient.

The correct answer: D

Hope this helps!

-Jay

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