Problem Solving

[GMAT math practice question]

In rectangle ABCD, as shown in the figure, the length of line AB was increased by 10% to make line AB' and line AD was decreased by 10% to make line AD'. What percentage is the reduced area of rectangle ABCD of the original area?

A. 1%
B. 5%
C. 10%
D. 15%
E. 17%

I took simple numbers to work on this one:

AB = 90, AD = 110 => Area of rectangle = 9900

After increasing AB by 10% and decreasing AD by 10%,

AB` = 99, AD` = 99 => Area of a square = 9801

So the area reduced by 10%.

=>

Assume the width and the length of the rectangle are a and b.
Since a is increased by 10%, a becomes 1.1a.
Since b is decreased by 10%, b becomes 0.9b.

The area of the rectangle ab becomes (1.1)(0.9)ab = 0.99ab.
So, we have (0.99ab - ab) / ab = -0.01, meaning the area decreased by 1%.

Therefore, A is the answer.
Answer: A

henilshaht wrote:I took simple numbers to work on this one:

AB = 90, AD = 110 => Area of rectangle = 9900

After increasing AB by 10% and decreasing AD by 10%,

AB` = 99, AD` = 99 => Area of a square = 9801

So the area reduced by 10%.

Sorry, I made a small mistake in the above example. In this scenario, the area has reduced by 1% and not 10%.