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factory original output

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by karyi » Sun Apr 12, 2020 2:45 am

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I came across this question in the Princeton Review - cracking the GMAT premium 2020 edition .

Here is the original question:

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 be 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) 70%

I tried to answer this question by plugging in 1000 as the original output, and i get 32% as my answer. However, the answer provided by this book is 24%, with no any explanation.
Can anyone show how does it get 24%? Why not 32% instead?

Thanks in advance.
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Re: factory original output

by jbryant62 » Mon Apr 13, 2020 1:08 pm
karyi wrote: ↑
Sun Apr 12, 2020 2:45 am
 I came across this question in the Princeton Review - cracking the GMAT premium 2020 edition .

Here is the original question:

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 be 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) 70%

I tried to answer this question by plugging in 1000 as the original output, and i get 32% as my answer. However, the answer provided by this book is 24%, with no any explanation.
Can anyone show how does it get 24%? Why not 32% instead?

Thanks in advance.
remember when dealing with percentages, its the rate of change/divided by the original amount. . so in your ex. new output is 1320. so rate of change back to 1000 is 1320-1000/1320 = 320/1320 =~24%
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Re: factory original output

by Scott@TargetTestPrep » Wed Apr 15, 2020 9:47 am
karyi wrote: ↑
Sun Apr 12, 2020 2:45 am
 I came across this question in the Princeton Review - cracking the GMAT premium 2020 edition .

Here is the original question:

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 be 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) 70%

I tried to answer this question by plugging in 1000 as the original output, and i get 32% as my answer. However, the answer provided by this book is 24%, with no any explanation.
Can anyone show how does it get 24%? Why not 32% instead?

Thanks in advance.
Let’s say the original output is n; after the increases, the new output is:

1.1 x 1.2 x n = 1.32n = (132/100)n

To reduce (132/100)n back to n, we must multiply by 100/132 since 132/100 x 100/132 = 1.

100/132 = 50/66 = 25/33 ≈ 76%

Thus we have to reduce the new output by 100% - 76% = 24% to restore the original output.

Answer: B

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