If y is an even integer and x is an odd integer, which of the following expressions could be an even integer?
(A) 3x + y/2
(B) (x + y)/2
(C) x + y
(D) x/4 − y/2
(E) x^2 + y^2
How will i solve this kind of problem?
OA A
If y is an even integer and x is an odd integer
This topic has expert replies
-
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
- elias.latour.apex
- Master | Next Rank: 500 Posts
- Posts: 228
- Joined: Thu Apr 20, 2017 1:02 am
- Location: Global
- Thanked: 32 times
- Followed by:3 members
- GMAT Score:770
Probably the easiest way to solve these types of problems is to run scenarios.
Let x, which must be odd, = 1
Let y, which must be even, = 2
(A) 3(1)+2/1 = 3+1 = 4
So (A) could be even. That's your answer. No need to test further.
Let x, which must be odd, = 1
Let y, which must be even, = 2
(A) 3(1)+2/1 = 3+1 = 4
So (A) could be even. That's your answer. No need to test further.
Elias Latour
Verbal Specialist @ ApexGMAT
blog.apexgmat.com
+1 (646) 736-7622
Verbal Specialist @ ApexGMAT
blog.apexgmat.com
+1 (646) 736-7622
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
Notice the problem is a "could be" problem, not a "must be" problem. Let's go through each answer choice, recalling that odd + odd = even, and odd + even = odd, and even + even = even.lheiannie07 wrote:If y is an even integer and x is an odd integer, which of the following expressions could be an even integer?
(A) 3x + y/2
(B) (x + y)/2
(C) x + y
(D) x/4 − y/2
(E) x^2 + y^2
A) 3x + y/2
3x is odd and y/2 could be odd (for example, if y = 6). Thus 3x + y/2 could be even.
The answer must be A. However, as an exercise, let' verify that none of the other four choices could be even. That is, they will never be even.
B) (x + y)/2
x + y is odd and thus (x + y)/2 is not even an integer (no pun intended).
C) x + y
x + y is odd.
D) x/4 - y/2
x/4 is not an integer and y/2 is an integer, but their difference will not be an integer.
E) x^2 + y^2
x^2 is odd and y^2 is even, but their sum will be odd. Recall here that odd x odd = odd and even x even = even.
Answer: A
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews