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%
OA B
Source: Princeton Review
The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output
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Say the original output was 100 units; thus, the output after it was increased by 10% = 110; similarly, the output after it was increased by 20% = 110 + 20% of 110 = 132.BTGmoderatorDC wrote: ↑Thu Jul 16, 2020 7:16 pmThe 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%
OA B
Source: Princeton Review
So, to reach the original output, we need to reduce the current output by 132 – 100 = 32.
Thus, percentage decrease in output = (32/132)*100% = time-consuming to compute.
Let's find out the approximate value.
Note that 20% of 132 = ~26 < 32. So, the correct answer must be greater than 20%; again, 30% of 132 = ~39 > 32. So, the correct answer must be less than 30%. Thus, the correct answer must be B (= 24%).
Correct answer: B
Hope this helps!
-Jay
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Solution:BTGmoderatorDC wrote: ↑Thu Jul 16, 2020 7:16 pmThe 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%
OA B
We can let the original output be 100. Therefore, by the holiday rush, its output is increased to:
100 x 1.1 x 1.2 = 132
Let p be the percent the new output has to be decreased in order to restore to the original output and we can create the equation:
(132 - 100)/132 = p/100
32/132 = p/100
132p = 3200
p = 3200/132 ≈ 24
Answer: B
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Let's plug in some NICE NUMBERS.BTGmoderatorDC wrote: ↑Thu Jul 16, 2020 7:16 pmThe 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%
OA B
Source: Princeton Review
Let's say the original output is 100 widgets.
- After a 10% increase the new output = 100 + 10 = 110 widgets
- After a 20% increase the output = 110 + 22 = 132 widgets
We want to get back to the original output.
In other words, we want to decrease from 132 widgets down to 100 widgets.
PERCENT CHANGE = 100(132 - 100 )/132
= 100(32/132)
ASIDE: 32/128 = 1/4 = 25%, so 32/132 must be a LITTLE LESS than 25%.
Take B
Cheers,
Brent