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# What fraction of the square region in the figure above is sh

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What fraction of the square region in the figure above is sh [#permalink]  06 Jul 2013, 01:48
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Difficulty:

25% (medium)

Question Stats:

59% (01:34) correct 41% (00:27) wrong based on 123 sessions
Attachment:

Square.png [ 16.99 KiB | Viewed 2427 times ]
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.

[Reveal] Spoiler:
What's the equation for statement 2?
[Reveal] Spoiler: OA

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Last edited by Bunuel on 06 Jul 2013, 01:52, edited 1 time in total.
Edited the question.
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Re: What fraction of the square region in the figure above is sh [#permalink]  06 Jul 2013, 01:58
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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 sh [#permalink]  06 Jul 2013, 02:01
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Expert's post

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:
Attachment:

Square 2.png [ 17.09 KiB | Viewed 2027 times ]
The shaded region is 1-1/4-1/8=5/8. Sufficient.

Hope it's clear.
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Re: What fraction of the square region in the figure above is sh [#permalink]  06 Mar 2014, 01:37
Expert's post
Bumping for review and further discussion.

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Re: What fraction of the square region in the figure above is sh [#permalink]  09 Mar 2014, 08:39
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.

Re: What fraction of the square region in the figure above is sh   [#permalink] 09 Mar 2014, 08:39
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