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Is the area of the rectangle less than 30 sq. inches?

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Is the area of the rectangle less than 30 sq. inches?

by gmattesttaker2 » Sun Nov 24, 2013 11:45 am
Hello,

Can you please assist with this:

Is the area of a rectangle less than 30 squares iches?
(1) The perimeter of the rectangle is less than 20 inches.
(2) The diagonal of the rectangle is less than 10 inches.


OA: A

My solution:
1) P = 2(l+w)
=> 20 = 2(l+w)
=> l+w = 10

Let, l = 8 and w = 1 => Area = 8 < 30
Let, l = 2 and w = 7 => Area = 14 < 30

Hence, Sufficient.

However, I was not sure how to proceed with 2. Can you please assist>

Thanks a lot,
Sri
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Source: — Data Sufficiency |
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by [email protected] » Sun Nov 24, 2013 6:18 pm
Hi Sri,

You can deal with Fact 2 in the same way that you deal with Fact 2: by TESTing Values.

Here, you have to be a bit more critical of the possibilities though:

Fact 2: the diagonal of the rectangle is less than 10

A diagonal line inside of a rectangle will create right triangles, so we can use the Pythagorean Theorem to figure out what the two sides COULD BE.

A^2 + B^2 < 100

To make the area as small as possible, we'll want one side to be really big and one side to be really small.

A = tiny fraction
B = Almost 10

Area = (tiny fraction)(Almost 10) = something less than 10
The answer to the question is YES

To make the area as big as possible, we'll want the two sides to be equal in length.

A = Almost root50
B = Almost root50

Area = (Almost root50(Almost root50) = Almost 50
The answer to the question is NO
Fact 2 is INSUFFICIENT

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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