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rawat2583: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Sat Jun 19, 2010 4:20 am

Geometry

by rawat2583 » Tue Mar 26, 2019 4:15 pm

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3 squares are overlapped one another with the same center shown as above. If all points intersected are midpoints, what fraction of the area of the largest square is the area of the region shaded?

A. 1/2 B. 1/3 C. 1/4 D. 1/5 E. 2/3

Source: Beat The GMAT — Problem Solving | Tue Mar 26, 2019 4:15 pm

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by GMATGuruNY » Tue Mar 26, 2019 4:55 pm

Each triangle in the figure above is an isosceles right triangle with sides 1, 1 and âˆš2.
Shaded region = 4 triangles.
Largest square = 16 triangles.
Thus:
(shaded region)/(largest square) = 4/16 = 1/4.

The correct answer is C.

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by Scott@TargetTestPrep » Wed Mar 27, 2019 6:06 pm

rawat2583 wrote:3 squares are overlapped one another with the same center shown as above. If all points intersected are midpoints, what fraction of the area of the largest square is the area of the region shaded?

A. 1/2 B. 1/3 C. 1/4 D. 1/5 E. 2/3

We can let the side of the largest square be 10. Thus the side of second largest square is 10/2 x âˆš2 = 5âˆš2 and the side of the smallest square is (5âˆš2)/2 x âˆš2 = 5. Now, the area of the largest, second largest and the smallest squares are 10^2 = 100, (5âˆš2)^2 = 50 and 5^2 = 25, respectively. The shaded area is the difference between the area of the second largest and smallest squares, so it's 50 - 25 = 25. Thus the fraction of the largest square is shaded is 25/100 = 1/4.

Answer: C

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