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Fence X is twice as long as fence Y, and fence Y...

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by BTGmoderatorLU » Sat Jan 06, 2018 1:55 pm
Fence X is twice as long as fence Y, and fence Y is two feet shorter that fence Z. If 3 feet were added to each fence, which of the following must be true?

I. X is twice as long as Y.
II. Y is 2 feet shorter than Z.
III. X is longer than Z.

A. I only
B. II only
C. III only
D. I and II
E. II and III

The Oa is B.

I'm confused with this PS question. Experts, any suggestion about the solution? Thanks in advance.
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by GMATGuruNY » Sat Jan 06, 2018 2:51 pm
LUANDATO wrote:Fence X is twice as long as fence Y, and fence Y is two feet shorter that fence Z. If 3 feet were added to each fence, which of the following must be true?

I. X is twice as long as Y.
II. Y is 2 feet shorter than Z.
III. X is longer than Z.

A. I only
B. II only
C. III only
D. I and II
E. II and III
Test the SMALLEST POSSIBLE CASE.
Let Y = 1.
Since X is twice as long as Y, X = 2Y = 2*1 = 2.
Since Y is 2 feet shorter than Z, Z = Y+2 = 1+2 = 3.

Adding 3 feet to each fence, we get:
New Y = 1+3 = 4.
New X = 2+3 = 5.
New Z = 3+3 = 6.

Since X=5 is not twice as long as Y=4, eliminate any answer choice that includes I.
Eliminate A and D.
Since X=5 is not longer than Z=6, eliminate any remaining answer choice that includes III.
Eliminate C and E.

The correct answer is B.
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