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Problem Solving

by phoenix9801 » Sat May 19, 2012 7:18 am
Anyone a good idea how to solve this problem. Thanks


On Tuesday, Carla's Cars sold 2/5 of the cars on the lot, including 1/3 of the hybrid cars. If hybrids made up ¼ of the cars on the lot on Tuesday, what fraction of the unsold cars were hybrids?

A) 1/12
B) 5/36
C) 1/6
D) 5/24
E) 5/18
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by Stuart@KaplanGMAT » Sat May 19, 2012 7:30 am
phoenix9801 wrote:Anyone a good idea how to solve this problem. Thanks


On Tuesday, Carla's Cars sold 2/5 of the cars on the lot, including 1/3 of the hybrid cars. If hybrids made up ¼ of the cars on the lot on Tuesday, what fraction of the unsold cars were hybrids?

A) 1/12
B) 5/36
C) 1/6
D) 5/24
E) 5/18
Hi!

We see a fraction question with unknown values. Perfect time to pick numbers!

First, let's identify the exact question: what fraction of UNSOLD cars were HYBRIDS. In other words, we want to solve for:

(# of unsold hybrids)/(total # of unsold cars)

To make the math work out, always pick a common denominator of the fractions. Here we have 5ths, 3rds and 4ths, so let's pick 3*4*5 = 60 cars.

So, we have a total of 60 cars on the lot. We know that 2/5 were sold, so 3/5 were unsold. Accordingly, the total number of unsold cars is 3/5(60) = 36.

There were a total of 1/4(60) = 15 hybrids on the lot. We know that 1/3 of the hybrids sold, so 2/3 of them didn't sell. Therefore, there are 2/3(15) = 10 unsold hybrids.

Plugging into the question:

(# of unsold hybrids)/(total # of unsold cars) = 10/36 = 5/18... choose E!
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