The GMAT Sample Math question is an arithmetic problem solving question from the topic percentages and fraction. The question deals with the concept of finding the percentage increase in area of a rectangle given percent change in its dimensions.
What is the % change in the area of a rectangle when its length increases by 10% and its width decreases by 10%?
A. 0%
B. 20% increase
C. 20% decrease
D. 1% decrease
E. Insufficient data
The correct choice is (D) and the correct answer is 1% decrease.
Whenever you encounter problems like this, use a numerical example and then proceed.
For ease of computation, it is safe in most cases, to assume the length to be 100 units and the width to be 100 units.
(Remember, a square is a rectangle too and the problem works the same way when you assume different values for length and width. Computation becomes a bit tedious with different values for length and width)
Area of a rectangle =
length * width = 100 * 100 = 10,000 sq units.
When the length increases by 10%, the new length becomes 110 units.
And as the width decreases by 10%, new width becomes 90 units.
Therefore, New area = 110 * 90 = 9900 sq units.
New area is 100 sq units lesser than the original area.
% change in area = ((change in area)/(original area)) * 100
= (100/10,000)*100 = 1% decrease in area
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