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If a rectangular region has perimeter P inches and area A sq

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Manager
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B
Joined: 23 Dec 2013
Posts: 235
Location: United States (CA)
GMAT 1: 710 Q45 V41
GMAT 2: 760 Q49 V44
GPA: 3.76
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Re: If a rectangular region has perimeter P inches and area A sq [#permalink]

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New post 16 Jul 2017, 10:47
olifurlong wrote:
If a rectangular region has perimeter P inches and area A square inches, is the region square?

(1) P = 4/3*A
(2) P = 4√A


The goal is to determine if the shape is in fact a square.

Statement 1) P = 4/3*(A)

If true, then P=4x and A = x^2

4x = 4/3*(x^2)
x = x^2/3
x = 3

Only true if the side is length 3. We don't know if the side of the shape has length 3, so the statement is insufficient.

Statement 2) P = 4sqrt(A)

4x = 4sqrt(x^2)
4x=4x
x = x

This statement is true, so the statement is sufficient.
Intern
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GMAT 1: 720 Q47 V42
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Re: If a rectangular region has perimeter P inches and area A sq [#permalink]

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New post 17 Jul 2017, 05:47
(B) in IMO. First assume the rectangle is a square. Then l=b. P=4l and Area=l^2. If you consider statement 1, LHS is not equal to RHS.
If you consider statement 2, LHS=RHS. So B is sufficient.
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Re: If a rectangular region has perimeter P inches and area A sq [#permalink]

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New post 29 Jan 2018, 03:13
This question raises very important point on DS questions.

First of all it is a YES/NO question.

When you plug in numbers statement (2) becomes YES. And when you plug numbers in statement (2) the answer is almost always no. Theoretically both statements give you concrete YES or NO, therefore each alone must be sufficient.

But two statements must both either say YES or NO. If one statement yields YES but the other NO, then the statement that you know for 100% is sufficient is the correct answer. And there must be at least on set of numbers that would give YES answer for statement one. But you should not bother to find that set of numbers.
Re: If a rectangular region has perimeter P inches and area A sq   [#permalink] 29 Jan 2018, 03:13

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If a rectangular region has perimeter P inches and area A sq

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