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% increase

This topic has 5 expert replies and 2 member replies
datonman Senior | Next Rank: 100 Posts Default Avatar
Joined
28 May 2014
Posted:
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% increase

Post Thu Jan 29, 2015 2:52 pm
Here's the 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 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%

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Vipul1991 Newbie | Next Rank: 10 Posts Default Avatar
Joined
02 May 2017
Posted:
6 messages
Post Sat Aug 12, 2017 9:38 am
100 ---> (10%) 100 X 0.1=110
110 ---> (20 %) 110 X 0.2=132

132-100= 32$ increase
(Change/Original)*100 = (32/132)*100= 24%

(B)

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GMAT/MBA Expert

Post Sat Jan 13, 2018 9:33 am
datonman wrote:
Here's the 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 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%
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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Post Wed Feb 11, 2015 12:22 pm
Hi datonman,

I'm a big believer in TESTing VALUES in these types of questions (as Brent and Mitch have both 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: B

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

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Post Wed Feb 11, 2015 9:34 am
j_shreyans wrote:
Hi All ,

I got the question but one thing:

% change formula is = 100(final value - initial value)/initial.

So we got 132 as final value and we have to be decreased in order to restore the original output i.e 100 which is initial value right?

so it should be 100(132-100)/100

Please advisve.

Thanks

Shreyans
When we compute a percent increase -- implying that we are STARTING FROM A SMALLER VALUE and increasing to a greater value -- the initial value is the SMALLER VALUE.
When we compute a percent decrease -- implying that we are STARTING FROM A GREATER VALUE and decreasing to a smaller value -- the initial value is the GREATER VALUE.

Question stem:
By approximately what percent would the output of the factory now have to be DECREASED in order to restore the original output?
Here, we are asked to compute a percent decrease, so the initial value is the GREATER VALUE.
Thus:
Percent decrease from 132 to 100 = (132-100)/132 * 100 ≈ 24.

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j_shreyans Legendary Member Default Avatar
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Post Wed Feb 11, 2015 9:15 am
Hi All ,

I got the question but one thing:

% change formula is = 100(final value - initial value)/initial.

So we got 132 as final value and we have to be decreased in order to restore the original output i.e 100 which is initial value right?

so it should be 100(132-100)/100

Please advisve.

Thanks

Shreyans

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Post Thu Jan 29, 2015 3:28 pm
datonman wrote:
Here's the 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 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%
Let the original output = 100.
After a 10% increase, the new output = 100 + 10% of 100 = 110.
After a further 20% increase, the holiday output = 110 + 20% of 110 = 132.

By approximately what percent would the output of the factory now have to be decreased in order to restore the original output?
Many students get confused when answering this type of question.
One way to avoid making a silly mistake is to PLUG IN THE ANSWERS.
When the holiday output of 132 is decreased by the correct answer choice, the result will be an output of 100 (the original output).
Start with an easy value in the middle.

Answer choice C: 30%
Holiday output reduced by 30% = 132 - 30% of 132 ≈ 132-40 = 92.
Here, the decrease is too BIG.
Since a smaller decrease is required, eliminate C, D and E.

Answer choice A: 20%
Holiday output reduced by 20% = 132 - 20% of 132 ≈ 132-26 = 106.
Here, the decrease is too SMALL.
Eliminate A.

The correct answer is B.

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GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
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For more information, please email me at GMATGuruNY@gmail.com.

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GMAT/MBA Expert

Post Thu Jan 29, 2015 3:11 pm
datonman wrote:
Here's the 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 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%
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

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

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