If wxyz 0, does the ratio of w to x equal the ratio of y to z?

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Thu Apr 28, 2022 10:06 pm

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If wxyz ≠ 0, does the ratio of w to x equal the ratio of y to z?

(1) w/y = x/z

(2) wy = xz

OA A

Source: Magoosh

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Source: Beat The GMAT — Data Sufficiency | Thu Apr 28, 2022 10:06 pm

gmat.prasanna: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Tue Aug 23, 2022 7:19 pm

Re: If wxyz 0, does the ratio of w to x equal the ratio of y to z?

by gmat.prasanna » Sat Sep 03, 2022 11:42 pm

By (1) we know that,
w/y=x/z
or, wz=xy (cross multiplication)
or, w/x=y/z

For all values this would hold true.

Sufficient

By (2) we know that,
w/x=z/y

At first glance we may think w/x = z/y means w/x is not equal to y/z, however, if we consider w=x=y=z=1, then w/x=1=y/z.

So for value= 1, w/x=z/y would not hold w/x=y/z for all values except when all variables = 1, however, we can consider this extreme to be possible since it meets the condition in the given question.

Hence insufficient.

Answer A

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