If x is an integer, is x + 2 even?

This topic has expert replies
Moderator
Posts: 7187
Joined: Thu Sep 07, 2017 4:43 pm
Followed by:23 members

If x is an integer, is x + 2 even?

by BTGmoderatorDC » Mon Apr 11, 2022 8:33 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

If x is an integer, is x + 2 even?

(1) x + 3 is an even integer.
(2) x − 2 is an odd integer.


OA D

Source: Princeton Review

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

BTGmoderatorDC wrote:
Mon Apr 11, 2022 8:33 pm
If x is an integer, is x + 2 even?

(1) x + 3 is an even integer.
(2) x − 2 is an odd integer.


OA D

Source: Princeton Review
Some important rules:
#1. ODD +/- ODD = EVEN
#2. ODD +/- EVEN = ODD
#3. EVEN +/- EVEN = EVEN


Target question: Is x + 2 even?

Statement 1: x + 3 is an even integer.
Since 3 is ODD, we can rewrite statement 1 as x + ODD = EVEN, which means x must be ODD, which means x + 2 must be odd
So, the answer to the target question is NO, x + 2 is not even
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x − 2 is an odd integer
Since 2 is EVEN, we can rewrite statement 2 as x - EVEN = ODD, which means x must be ODD, which means x + 2 must be odd
So, the answer to the target question is NO, x + 2 is not even
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D
Brent Hanneson - Creator of GMATPrepNow.com
Image