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

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Board of Directors
Joined: 01 Sep 2010
Posts: 3454
The output of a factory was increased by 10% to keep up with [#permalink]

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11 Sep 2012, 12:39
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Difficulty:

65% (hard)

Question Stats:

55% (01:13) correct 45% (00:39) wrong based on 251 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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Director
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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, 23:32
2
KUDOS
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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Manager
Joined: 18 Oct 2011
Posts: 88
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Re: The output of a factory was increased by 10% to keep up with [#permalink]

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04 Jan 2013, 14:09
1
KUDOS
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.
Intern
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GMAT Date: 04-20-2013
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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, 10:23
1
KUDOS
(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, 02:52
1
KUDOS
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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Director Status: Tutor - BrushMyQuant Joined: 05 Apr 2011 Posts: 611 Location: India Concentration: Finance, Marketing Schools: XLRI (A) GMAT 1: 700 Q51 V31 GPA: 3 WE: Information Technology (Computer Software) Re: The output of a factory was increased by 10% to keep up with [#permalink] ### Show Tags 11 Sep 2012, 19:39 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% 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! _________________ Ankit Check my Tutoring Site -> Brush My Quant GMAT Quant Tutor How to start GMAT preparations? How to Improve Quant Score? Gmatclub Topic Tags Check out my GMAT debrief How to Solve : Statistics || Reflection of a line || Remainder Problems || Inequalities Board of Directors Joined: 01 Sep 2010 Posts: 3454 Re: The output of a factory was increased by 10% to keep up with [#permalink] ### Show Tags 12 Sep 2012, 01:31 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 _________________ Manager Joined: 24 Jul 2011 Posts: 75 Location: India Concentration: Strategy, General Management GMAT 1: 670 Q49 V33 WE: Asset Management (Manufacturing) Re: The output of a factory was increased by 10% to keep up with [#permalink] ### Show Tags 12 Sep 2012, 09:01 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. _________________ My mantra for cracking GMAT: Everyone has inborn talent, however those who complement it with hard work we call them 'talented'. +1 Kudos = Thank You Dear Are you saying thank you? Intern Joined: 03 Jan 2013 Posts: 15 Re: The output of a factory was increased by 10% to keep up with [#permalink] ### Show Tags 03 Jan 2013, 15:07 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 Intern Joined: 08 Jul 2015 Posts: 31 Location: India Concentration: Finance GMAT 1: 690 Q50 V32 GMAT 2: 750 Q51 V40 GPA: 3.58 Re: The output of a factory was increased by 10% to keep up with [#permalink] ### Show Tags 24 Apr 2016, 03:29 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 EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 10763 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: The output of a factory was increased by 10% to keep up with [#permalink] ### Show Tags 10 Jan 2018, 19:10 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: [Reveal] Spoiler: B GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Joined: 11 Sep 2015
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Re: The output of a factory was increased by 10% to keep up with [#permalink]

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13 Jan 2018, 09:34
Expert's post
Top Contributor
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?

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

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
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Re: The output of a factory was increased by 10% to keep up with   [#permalink] 13 Jan 2018, 09:34
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