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Rectangular Frame.

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Rectangular Frame.

by sumitkhurana » Thu Jan 29, 2009 6:44 am
A rectangular frame encloses a picture. What
is the length in inches of the picture?

(1) The frame measures 24 inches by 18 inches.
(2) Area of the frame = area of the picture it
encloses.
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Source: — Data Sufficiency |
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by DanaJ » Thu Jan 29, 2009 8:09 am
1. is insufficient because the frame could be thicker than the picture.
2. is insufficient because we do not know any numbers.

Put together, the two are again insufficient, since we do not know if the length is the side with 24 inches or the side with 18 inches.
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Re: Rectangular Frame.

by Stuart@KaplanGMAT » Thu Jan 29, 2009 12:55 pm
sumitkhurana wrote:A rectangular frame encloses a picture. What
is the length in inches of the picture?

(1) The frame measures 24 inches by 18 inches.
(2) Area of the frame = area of the picture it
encloses.
I agree that the answer is (E), but for different reasons.

When we combine the statements, we know that the area of the frame + the area of the picture is 24*18. Since the frame and the picture have the same area, we know that each has an area of (24*18)/2.

However, we have no idea whether the frame has uniform thickness. If the frame did have uniform thickness, we could determine the exact dimensions of the picture (and by mathematical convention, "length" would be the larger of the two dimensions). Without knowing this fact, there are an infinite number of ways we could meet the criteria in the statements.
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