Bunuel wrote:
The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output is increased by 20%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output?
A. 20%
B. 24%
C. 30%
D. 32%
E. 79%
Let original output \(= P\)
Initial increase = 10% \(= 1.1*P\)
Increase due to holiday rush = additional 20% \(= 1.2*1.1*P = 1.32P\)
Now we need to decrease this back down to the original output \(P\)
We could do:
\(1.32P * (1-x) = P\), where \(x\) is the decrease to the output
\(x=1-\frac{1}{1.32} = \frac{1.32-1}{1.32} = \frac{0.32}{1.32}\)
\(x=0.24 = 24\)%
Answer: B
OR, we can avoid the long division by recognizing that the expression \(\frac{0.32}{1.32}\) will be just slightly less than \(\frac{1}{4} = 25\)%
\((\frac{0.33}{1.32} = \frac{1}{4})\)
The only answer choice that fits is B: 24%
Of course this estimation wouldn't work as well if the answer choices were closer together, but in this case it could be a convenient shortcut to avoid some long division.
_________________
Dave de Koos
GMAT aficionado