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What is the perimeter of quadrilateral Q?

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Joined: 02 Sep 2009
Posts: 50009
What is the perimeter of quadrilateral Q?  [#permalink]

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New post 17 Oct 2016, 05:54
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

76% (00:42) correct 24% (00:52) wrong based on 95 sessions

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Manager
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Joined: 28 Jun 2016
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Location: Canada
Concentration: Operations, Entrepreneurship
Re: What is the perimeter of quadrilateral Q?  [#permalink]

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New post 17 Oct 2016, 06:05
Statement 1:

Insufficient

Statement 1:

If Q is square, P = 20

If Q is rectangle of 25x1, P=52

Insufficient

St1&2:

Same scenarios as statement 2

Insufficient

E


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Re: What is the perimeter of quadrilateral Q?  [#permalink]

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New post 17 Oct 2016, 06:18
Bunuel wrote:
What is the perimeter of quadrilateral Q?

(1) Q is a rectangle.

(2) The area of Q is 25.



The key concept is to understand that the perimeter/area ratio decreases as the length and breadth of a rectangle converge: The minimum perimeter/area ratio is when the rectangle is a perfect square. Therefore, for a given area of a rectangle, its perimeter can be known only if the ratio of the length and breadth are known.

Statement (1) alone is insufficient, since we don't know the area nor its ratio;
Statement (2) alone is insufficient, since we don't know the type of quadrilateral, nor its perimeter, nor the ratio of the perimeter;
Both statements are insufficient also since we still don't know the ratio of the length and breadth.

Therefore the answer is (E)
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Re: What is the perimeter of quadrilateral Q?  [#permalink]

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New post 09 Feb 2018, 07:40
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Top Contributor
Bunuel wrote:
What is the perimeter of quadrilateral Q?

(1) Q is a rectangle.

(2) The area of Q is 25.


Target question: What is the perimeter of quadrilateral Q?

If we recognize that each statement alone is not sufficient, we can jump straight to......

Statements 1 and 2 combined
There are several quadrilaterals satisfy BOTH statements. Here are two:
Case a: Q is a rectangle with width 1 and length 25. In this case, the perimeter of quadrilateral Q is 1 + 1 + 25 + 25 = 52
Case b: Q is a rectangle with width 5 and length 5. In this case, the perimeter of quadrilateral Q is 5 + 5 + 5 + 5 = 20
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

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Re: What is the perimeter of quadrilateral Q? &nbs [#permalink] 09 Feb 2018, 07:40
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What is the perimeter of quadrilateral Q?

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