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## If w, x, y and z are integers such that w/x and y/z are inte

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### Top Member

ardz24 Master | Next Rank: 500 Posts
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#### If w, x, y and z are integers such that w/x and y/z are inte

Sun Sep 24, 2017 2:37 am
If w, x, y and z are integers such that w/x and y/z are integers, is w/x + y/z odd?

(1) wx + yz is odd
(2) wz + yx is odd

Any of the options alone is sufficient? Can any expert explain?

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### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
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Sun Sep 24, 2017 2:50 am
Quote:
If w, x, y and z are integers such that w/x and y/z are integers, is w/x + y/z odd?

(1) wx + yz is odd
(2) wz + yx is odd
Before we evaluate the two statements, we should examine how the question stem can be rephrased.

w/x + y/z = (wz + xy)/xz.
Since w/x and y/z are integers, their sum (w/x + y/z) is an integer.
Thus, (wz + xy)/xz must also be an integer.

The question becomes: Is integer w/x + y/z -- which can be rephrased as (wz + xy)/xz -- odd?

Statement 1: wx + yz = odd.
Let w=1, x=1, y=2 and z=2, so that wx + yz = 1*1 + 2*2 = 5.
Is w/x + y/z odd?
NO, since 1/1 + 2/2 = 2.

Let w=1, x=1, y=6, and z=3, so that wx + yz = 1*1 + 6*3 = 19.
Is w/x + y/z odd?
YES, since 1/1 + 6/3 = 3.
INSUFFICIENT.

Statement 2: wz + xy = odd.
Please note the values highlighted in red:
Just as 10/2=5 is a factor of 10, and 12/3=4 is a factor of 12, so too is (wz + xy)/xz a FACTOR of wz + xy.

Since wz + xy is odd, all of its factors must be odd.
Thus, (wz + xy)/xz must be odd.
SUFFICIENT.

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Thanked by: ardz24
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