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Percentage Problem

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by melguy » Mon Jun 17, 2013 5:53 am
A reduction of 20% in the price of apples could enable a man to get 120 more for 1440 bucks. Find the first price of one apple.

Please help me with this questions. By long calculation I took more than 10 mins. Kindly suggest some quick method.
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by Brent@GMATPrepNow » Mon Jun 17, 2013 6:10 am
melguy wrote:A reduction of 20% in the price of apples could enable a man to get 120 more for 1440 bucks. Find the first price of one apple.
One (potentially fast) approach would be to plug in the answer choices, but you have not supplied them.

Let A = original price per apple

We'll use two facts.
#1) Number of apples purchased = ($1440)/(apple price)
#2) After a 20% reduction, the new price is 0.8A

If A 20% price reduction enables a man to buy 120 extra apples, then we can write the following "word" equation:
(# of apples bought at reduced price) - (# of apples bought at original price) = 120
So, 1440/0.8A - 1440/A = 120
Get common denominator of 4A: (5)(1440)/4A - (4)(1440)/4A = 120
Simplify left side: 1440/4A = 120
Reduce left side: 360/A = 120
A = 3

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by melguy » Mon Jun 17, 2013 8:21 am
Thanks Brent.

My apologies that I did not have the answer choices. Once I saw the answer it was pretty easy plugging back the number and fitting the numbers to where they belong (thanks to the shortcut you have mentioned in your videos of finding the % quickly).
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by Brent@GMATPrepNow » Mon Jun 17, 2013 9:15 am
melguy wrote: . . .thanks to the shortcut you have mentioned in your videos of finding the % quickly
If anyone is interest, the video melguy is referring to is a free video you can find here https://www.gmatprepnow.com/module/gmat- ... ic?id=1073. The part about finding percents quickly begins around 3:00

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