GMAT Quant Questions | Percentages Q9

GMAT Sample Questions | Percentages | Geometry

The given question is a GMAT 500-550 level problem solving question in Percents. This GMAT practice question tests the concept of finding the percentage increase in area of a rectangle given percent change in its dimensions.

Question 9: What is the % change in the area of a rectangle when its length increases by 10% and its width decreases by 10%?

  1. 0%
  2. 20% increase
  3. 20% decrease
  4. 1% decrease
  5. Insufficient data

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Explanatory Answer | GMAT Percentage Q9

Note: Whenever you come across questions such as this, assume values for length and width. If all data given is in percent, assume some measure to be 100.
Let the length be 100 units and the width be 100 units.

Remember, a square is a also rectangle and the answer will be same whether or not you assume same values for the length and the width of the rectangle. Computation becomes easier when you assume same values for both the length and width.

Area of a rectangle = length × width = 100 × 100 = 10,000 sq units.
The length increases by 10%; the new length will be 100 + 10% of 100 = 110 units.
The width decreases by 10%; the new width will be 100 - 10% of 100 = 90 units.

Therefore, new area = 110 × 90 = 9900 sq units.
New area is 100 sq units lesser than the original area.

% change in area = \\frac{\text{change in area}}{\text{original area}}) × 100
= \\frac{100}{10,000}) × 100 = 1% decrease in area

The area of a rectangle decreases by 1%

Choice D is the correct answer.

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