factory original output

[karyi]

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.

[jbryant62]

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%

[Scott@TargetTestPrep]

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