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

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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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:

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Rich
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