OK...this one might be to simple but is taking my brains out

[aakarim]

Hello everyone
I have just now seriously started my maths prep for the GMAT. Since I have been out of touch with maths for like 10 years, I am struggling abit..but still am standing strong and committed. I am sure with practice I should be fine....

OK I have started with Princeton review ( as I have not been able to get my hands as yet on the OG11). Anyhow..on page 70, there is a upper-medium problem which goes like this:

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

choices: 20%,24%,30%,32% and 70%.


The answer the book states is 24% ...could any of my fellow friends out there in this whole world kindly explain to me HOW DID HE GET THIS ANSWER.....its not mentioned anywhere in the book how he cracked it..


this question might be too simple ..but its really making my brain twist...

thanks and regards
Dr. Arsalan

[chiller]

Hey aakarim,

Here is my take on it.

Ok, so lets assume output (x) = 100.

As a result,
Output was increased 10%, therefore 1.10x = 110.
Output was then increased another 20% for holiday rush, therefore 1.20(110) = 132 (final output).

Now, the question is asking what % is required to take 132 down to 100, so setup the following equation.

132/100 = 100/x
132x = 10000
x = 75.7.

Therefore, 100 represents 75.7 percent of 132, hence it is a decrease of '24%' to get back to original output.

Hope this helps.

[aakarim]

Hello Chiller
Thanks for the reply. I understand till the point you calculated the 132 percent. Ok.... Everything good.....

I also understand you got the answer but one thing i could not grab is that how did you draft that formula. Could u just briefly explain that.


Thanks
Dr. Arsalan

[Ian Stewart]

We can find the percentage directly. If we begin, say, with 100, increasing this by 10%, and then by 20%, we end up with 132. To get back to 100, we need to decrease this value by 32. What percentage is 32 of 132? Divide 32 by 132:

32/132 = 8/33 = 0.2424...

And as a percentage, this is approximately 24%.

I computed the decimal above, but there's no need to actually compute the decimal here. You could notice that 8/33 is just slightly smaller than 8/32 = 1/4 = 0.25, so among the answer choices, only 24% can be correct.

[aakarim]

Wooh Ian....you rock !!!!
Thanks a million !!!!.... I am totally



Dr. Arsalan