BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 641
Joined: Tue Feb 14, 2012 3:52 pm
Thanked: 11 times
Followed by:8 members

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
Top
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

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]
Image
Top
Post new topic Post Reply
• Page 1 of 1