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# What fraction of the square region in the figure above is shaded?

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What fraction of the square region in the figure above is shaded?  [#permalink]

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Updated on: 27 Feb 2018, 10:41
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Difficulty:

35% (medium)

Question Stats:

63% (00:58) correct 37% (00:54) wrong based on 236 sessions

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What fraction of the square region in the figure above is shaded?

(1) The area of the square region is 36
(2) P and Q are midpoints of two sides of the square as shown.

What's the equation for statement 2?
Attachment:

Square.png [ 16.99 KiB | Viewed 16938 times ]

Originally posted by fozzzy on 06 Jul 2013, 02:48.
Last edited by Bunuel on 27 Feb 2018, 10:41, edited 2 times in total.
Edited the question.
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What fraction of the square region in the figure above is sh  [#permalink]

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06 Jul 2013, 03:01
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1

What fraction of the square region in the figure above is shaded?

(1) The area of the square region is 36. We don't know positions of P and Q. Not sufficient.

(2) P and Q are midpoints of two sides of the square as shown. Look at the diagram below:

The shaded region is 1-1/4-1/8=5/8. Sufficient.

Hope it's clear.

Attachment:

Square 2.png [ 17.09 KiB | Viewed 14511 times ]

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Re: What fraction of the square region in the figure above is shaded?  [#permalink]

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06 Jul 2013, 02:58
2
fozzzy wrote:
What's the equation for statement 2?

Consider a side of length 2: $$Area=4$$; the midpoint divide each side into two segments of length 1.

Triangle pqLeft point has an Area of $$\frac{1}{2}$$, the other not shaded triangle (the one to the right of Q) has an area of $$1$$.

Shaded Area$$=4-1-0.5=2.5$$ => fraction $$\frac{2.5}{4}$$
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Re: What fraction of the square region in the figure above is shaded?  [#permalink]

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06 Mar 2014, 02:37
Bumping for review and further discussion.

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Re: What fraction of the square region in the figure above is shaded?  [#permalink]

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09 Mar 2014, 09:39
Because this is a square, we know the white shapes must be right triangles. If we can figure out what fraction of the square they occupy, we can find the requested area by subtracting this fraction from 1. What are the dimensions of the legs of each triangle?

Statement 1 gives us no information about the dimensions of the triangles. Insufficient.

Statement 2 tells us that the smaller triangle is 45-45-90 with each leg equal to s/2 (where s is the side of the square). We also know that the larger triangle has legs s and s/2. We can solve for each area in terms of s. We can therefore directly compare the are of the triangles to the area of the square. Sufficient.

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Re: What fraction of the square region in the figure above is shaded?  [#permalink]

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20 Sep 2016, 12:40
B is correct. Here's why:

(1) The area of the square region is 36 - INSUFFICIENT - we don't know whether P and Q are midpoints to calculate area of shaded region relative to whole

(2) P and Q are midpoints of two sides of the square as shown - SUFFICIENT - from this we can say each side it s (therefore each midpoint is 1/2 s) --> shaded area will be s^2 - [(1/2)(1/2 s)(1/2 s)+((1/2)(1/2 s)(s)]
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Re: What fraction of the square region in the figure above is shaded?  [#permalink]

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01 Mar 2019, 10:19
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: What fraction of the square region in the figure above is shaded?   [#permalink] 01 Mar 2019, 10:19
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