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

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The output of a factory was increased by 10% to keep up with [#permalink]

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11 Sep 2012, 13:39
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Difficulty:

65% (hard)

Question Stats:

51% (01:09) correct 49% (00:41) wrong based on 249 sessions

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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?

A. 20%
B. 24%
C. 30%
D. 32%
E. 79%

This question is possible in the real gmat ?? what is the level ?? I guess sub 600 but for me is even more less. However, it is classified as upper medium level
[Reveal] Spoiler: OA

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Re: The output of a factory was increased by 10% to keep up with [#permalink]

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11 Sep 2012, 20:39
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%

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

Hope it helps!
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Re: The output of a factory was increased by 10% to keep up with [#permalink]

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12 Sep 2012, 00:32
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carcass wrote:
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%

This question is possible in the real gmat ?? what is the level ?? I guess sub 600 but for me is even more less. However, it is classified as upper medium level

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%.

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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Re: The output of a factory was increased by 10% to keep up with [#permalink]

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12 Sep 2012, 02:31
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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Re: The output of a factory was increased by 10% to keep up with [#permalink]

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12 Sep 2012, 10:01
carcass wrote:
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

Here "original output" should be 100, instead of 110 as we are starting with 100.
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Re: The output of a factory was increased by 10% to keep up with [#permalink]

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03 Jan 2013, 16:07
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

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Re: The output of a factory was increased by 10% to keep up with [#permalink]

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04 Jan 2013, 15:09
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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.

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Re: The output of a factory was increased by 10% to keep up with [#permalink]

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31 Jan 2013, 11:23
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(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
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The output of a factory was increased by 10% to keep [#permalink]

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03 Jun 2013, 03:52
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Expert's post
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
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Re: The output of a factory was increased by 10% to keep up with [#permalink]

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Re: The output of a factory was increased by 10% to keep up with [#permalink]

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24 Apr 2016, 04:29
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

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Re: The output of a factory was increased by 10% to keep up with   [#permalink] 24 Apr 2016, 04:29
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