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14 Jan 2020, 05:21
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A
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Difficulty:
45%
(medium)
Question Stats:
57% (01:49) correct
43%
(01:31)
wrong
based on 67
sessions
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Does the rectangle have an area less than 30 unit^2?
(1) The perimeter of the rectangle is 20 units
(2) The length of the diagonal of the rectangle is 10 units
Are You Up For the Challenge: 700 Level Questions
(1) The perimeter of the rectangle is 20 units
(2) The length of the diagonal of the rectangle is 10 units
Are You Up For the Challenge: 700 Level Questions
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
14 Jan 2020, 09:14
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Bunuel
Is Area < 30?
Note: Area of rectangle is maximum when rectangle is a square
(1) The perimeter of the rectangle is 20 units
If the rectangle is a square.
each side = \(\frac{20}{4} = 5\) units
--> Maximum area possible = \(5^2 = 25\) units
--> Area is ALWAYS < 30 units --> A Definite NO --> Sufficient
(2) The length of the diagonal of the rectangle is 10 units
Case 1: When rectangle is a square
--> \(\sqrt{2}\)*side = \(10\)
--> side = \(5\sqrt{2}\)
--> Area = \((5\sqrt{2})^2 = 50\) units
Case 2: Least area will be close to zero.
Note that, as length of the rectangle approaches towards 10 units, breadth of the rectangle tends to be negligible (close to 0)
--> Area = 0 approximately
So, Area can be >30 or <30 --> Insufficient
Option A
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