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Fraction of Square

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by tonebeeze » Tue Mar 08, 2011 10:42 am
Please refer to Attachment

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.

OA: B

Can someone please walk me through the math for Statement 2. Thanks
Attachments
Screen shot 2011-03-08 at 9.47.18 AM.png
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Source: — Data Sufficiency |
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by clock60 » Tue Mar 08, 2011 11:09 am
hi tonebeeze
that is a good problem, and i initially solved it wrong, bad on me, and never be in a hurry
as for solution to the st 2
(2) general plan to calculate the area of each triangle, sum areas, and substract them from the area of square, and at last find the ratio
say the side of the square=x, then the area of the right triangle (i mean that is to the right, but it is also right)
S1=1/2*x*(x/2)=(x^2)/4
the area of the left triangle well
S2=1/2*(x/2)*(x/2)=(x^2)/8, now sum them
S1+S2=x^2/4+x^2/8=(3*x^2)/8. substract from the area of square
x^2-(3*x^2/8)=(5*x^2)/8-it is shaded area, and at last find the ratio
(5*x^2/8)/x^2, cancel x^2 and left with 5/8
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by GMATGuruNY » Tue Mar 08, 2011 11:12 am
tonebeeze wrote:Please refer to Attachment

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.

OA: B

Can someone please walk me through the math for Statement 2. Thanks
Statement 1: A = 36.
No way to determine what fraction of the area is shaded.
Insufficient.

Statement 2: P and Q are midpoints.

Image

The drawing above shows that the unshaded portions represent 1/8 and 1/4 of the area.
Thus, the shaded portion is 1 - 1/8 - 1/4 = 5/8 of the square.
Sufficient.

The correct answer is B.
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by clock60 » Tue Mar 08, 2011 11:16 am
hi GmatGuruNY
elegant and amazing!!!!!! i even can`t think this way
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