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by kris610 » Tue Feb 08, 2011 2:04 pm
The ratio of the area of a square mirror to its frame is 16 to 33. If the frame has a uniform width (c) around the mirror, which of the following could be the value, in inches, of c ?

I. 2
II. 3 1/2
III. 5

I only

III only

I && II only

I && III only

I, II && III
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by GMATGuruNY » Tue Feb 08, 2011 3:02 pm
kris610 wrote:The ratio of the area of a square mirror to its frame is 16 to 33. If the frame has a uniform width (c) around the mirror, which of the following could be the value, in inches, of c ?

I. 2
II. 3 1/2
III. 5

I only

III only

I && II only

I && III only

I, II && III
There is no math to be done here; just use common sense. Why couldn't the width of the frame be any value? We could choose a width for the frame, then shrink or expand the mirror until the ratio of mirror:frame = 16:33.

The correct answer is E.
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by Night reader » Tue Feb 08, 2011 3:57 pm
mirror side=a
frame side=b
width=c, b=a+2c, find c-?
a^2/(b^2-a^2)=16/33 ---> a^2/(a^2+4ac+4c^2-a^2)=16/33 ---> a^2/(4ac+4c^2)=16/33; a^2=64/33 *(c^2+ac) OR a^2=1.9(c^2+ac); if we substitute c={2, 7/2, 5} we get a real positive number for a, so choice E fits.

:) besides I don't think this is a real GMAT like question ---> "The ratio of the area of a square mirror to its frame's square"

kris610 wrote:The ratio of the area of a square mirror to its frame is 16 to 33. If the frame has a uniform width (c) around the mirror, which of the following could be the value, in inches, of c ?

I. 2
II. 3 1/2
III. 5

I only

III only

I && II only

I && III only

I, II && III
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