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

Question

https://gmatclub.com/forum/download/file.php?id=20475 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? Square.png

Bunuel · Accepted Answer

https://gmatclub.com/forum/download/file.php?id=20475 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: https://gmatclub.com/forum/download/file.php?id=20476 The shaded region is 1-1/4-1/8=5/8. Sufficient. Answer: B. Hope it's clear. Square 2.png

Zarrolou · Answer

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}

Bunuel · Answer

Bumping for review and further discussion.

GEOMETRY: Shaded Region Problems!

CCMBA · Answer

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.

The answer is B.

law258 · Answer

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 -

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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?

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