Official Solution:If one side of a rectangle was reduced by 20%, by how much does the other side have to be increased so that the area of the rectangle would not change?A. 18%
B. 20%
C. 24%
D. 25%
E. 30%
If \(a\) and \(b\) represent the original side lengths, then after reducing one side, the rectangle's area becomes \((0.8a) * b = \frac{4}{5}(ab)\). Consequently, the other side, \(b\), must become \(\frac{5}{4}b=1.25b\), which constitutes an increase by 25% to maintain the new area as \(ab\):
\((0.8a)(1.25b) = ( \frac{4}{5}a) (\frac{5}{4}b) = ab\).
Note that this is not a Geometry question. While it uses basic knowledge of lines and figures, it is a Percent Word Problem question. There are 8 questions within GMAT Prep Focus Edition that use similar principles.
Here is one example.
Answer: D