The output of a factory was increased by 10% to keep up with

Assume that the output is 100. After the first increase, it is 110. 20% increase of 110 is 22, so the new output is 132 (10% of 110 is 11, so 20% is 2*11=22).
To restore the initial output of 100, we need to reduce the new output 132 by 32. This represents 32/132, which is close but a little bit less than to 32/128 =25%.

Answer B.

Maybe the statistics show that people don't like so much % questions and/or they are not so good at them.
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The output of a factory was increased by 10% to keep up with rising demand. To handle the holiday rush, this new output was increased by 20%. By approximately what percent would the output now have to be decreased in order to restore the original output?

Let initial output is O then after 10% increase it will be 1.1O and after 20% increase on this new output the latest output will be 1.1O * 1.20 = 1.32O

Now we have to decrease the output by some percentage so that the new output is same as the starting output (O)

so, 1.32O * (1-x/100) = O

=> x = 24.24%

So, answer will be B

According to me its a 600-700 level question. And i guess it can come in gmat.

Hope it helps!
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Ok

Main issue is the fact that this problem was medium hard level. I was not sure about this

I resolved it without problems.

Regarding the solution, when you reach 132 to restore to the original output you have to take this new value to 110. So, the question says "By approximately " so we can estimate: 22%. A is not possible so the only that fits the bill is B, without necessary calculation

Thanks
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Here "original output" should be 100, instead of 110 as we are starting with 100.

I have to ask while solving the question and reading the solutions is there a "base equation" behind the following setup: x/100(132) = 32

what I can deduce is is : Original output percentage * final output = percentage to decrease output . I cant remember on the top of my head but I swear that its reminds me of the X or some number is n sort of setup ..anyone no or is this just a general equation that is automatically created to solve the problem

Thanks everyone

Difficulty levels are pretty subjective IMO. Everyone has their weak areas that they need to work on which might not hold significance for the next person.

(Explanation below provided by 'The Little Green Math Book')

Percentage decrease to return to an original number = \(\frac{New-Old}{New}\)

So: \(\frac{132-100}{132}\)= \(\frac{32}{132}\) ≈ 24% = B

Responding to a pm:

The output of a factory was increased by 10% to keep up with rising demand. To handle the holiday rush, this new output was increased by 20%. By approximately what percent would the output now have to be decreased in order to restore the original output?

20%
24%
30%
32%
79%

The original output increases by 10% and then 20%.

Method 1:

Holiday output = Old output * (11/10) *(6/5) = Old output * (33/25)

Now if you want to go back to the old output, you need to multiply the Holiday output by (25/33) i.e. reduce it by 8/33 which is approximately 24% (note that 8/33 = 24/99 i.e. approx 24%)

Holiday output * (25/33) = Old output * (33/25) * (25/33) = Old output

Method 2:

Or, use the formula.

Total % change = a + b + ab/100
Total % change = 10 + 20 + 10*20/100 = 32%

Now, you want to change it to 0, so,

0 = 32 + x + 32x/100
x = -32(100)/132 = 24% approximately

answer is B

Let the output of a factory is 100

First,increased by 10 %=110

due to holiday rush,it increase by 20%=110+22=132

132-(x/100*132)=100

24.24

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.

take it as original output =100.

to meet demand increase by 10%, then output=110.

to meet holiday demand , new output increase by 20% then output equals 132

To restore new holidy demand output to original 100.


final -initial/final*100
=32/132*100=8/33*100=24% approxiamately.

option B is correct.

Another approach

We have to decrease the output by 32.

Lets check option C first.

30% of 132 = 39.6 > 32

So, we will check option A now (as it will require less computation compared with option B)

20% of 132 = 26.4 < 32

Hence, option B is the answer

good quality question. critical thinking is must in these type of questions

Hi All,

I'm a big believer in TESTing VALUES in these types of questions (as EvaJager has shown). Since this question is rooted in algebra and arithmetic, you can solve it that way too:

We're told that the output of a factory is increased by 10%....

X = Original Output
X + 0.1X = 1.1X = New Output

Next, we're told that the new output is raised by 20%....

1.1X = New Output

1.1X + (0.2)(1.1X) =
1.1X + .22X =
1.32X = Final Output

We're asked to reduce this final output back down to the original output, so we need the Percentage Change Formula:

Percentage Change = (New - Old)/Old

(X - 1.32X)/(1.32X) = -.32X/1.32X = -32/132 = about -1/4 = about -25%

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Let's plug in some NICE NUMBERS.

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

100/100*110*120/100=132.
From
132,have to reduce 32

So..... 32/132*100=24%

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