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A parking garage has places for a certain number of cars. If [#permalink]

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17 Sep 2010, 01:05

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A parking garage has places for a certain number of cars. If \(\frac{1}{5}\) of the places are left empty, and \(\frac{2}{5}\) of the places are used by compact cars, non-compact cars take up what fraction of the filled spaces in the garage?

A. \(\frac{1}{3}\) B. \(\frac{2}{5}\) C. \(\frac{1}{2}\) D. \(\frac{3}{5}\) E. \(\frac{4}{5}\)

A parking garage has places for a certain number of cars. If \(\frac{1}{5}\) of the places are left empty, and \(\frac{2}{5}\) of the places are used by compact cars, non-compact cars take up what fraction of the filled spaces in the garage?

A. \(\frac{1}{3}\) B. \(\frac{2}{5}\) C. \(\frac{1}{2}\) D. \(\frac{3}{5}\) E. \(\frac{4}{5}\)

As \(\frac{1}{5}\) of the places are left empty then \(\frac{4}{5}\) of the places are filled --> \(\frac{2}{5}\) of the places are used by compact cars, so \(\frac{4}{5}-\frac{2}{5}=\frac{2}{5}\) are used by non-compact cars, which means that non-compact cars take \(\frac{\frac{2}{5}}{\frac{4}{5}}=\frac{1}{2}\) of the filled spaces in the garage.

Or just pick some smart number for total places, let it be 5, then 1 place is left empty, so 4 places are used --> 2 places are used by compact cars and 2 by non-compact cars, so non-compact cars take \(\frac{2}{4}=\frac{1}{2}\) of the filled spaces in the garage.

A parking garage has places for a certain number of cars. If \(\frac{1}{5}\) of the places are left empty, and \(\frac{2}{5}\) of the places are used by compact cars, non-compact cars take up what fraction of the filled spaces in the garage?

A. \(\frac{1}{3}\) B. \(\frac{2}{5}\) C. \(\frac{1}{2}\) D. \(\frac{3}{5}\) E. \(\frac{4}{5}\)

Empty = \(\frac{1}{5}\)

Compact cars = \(\frac{2}{5}\)

Non compact = \(1- \frac{1}{5} -\frac{2}{5}\) = \(\frac{2}{5}\)

Total filled spaces = \(\frac{2}{5}\) + \(\frac{2}{5}\) = \(\frac{4}{5}\)

fraction of the filled spaces in the garage by non compact cars = \(\frac{2}{5}\)/\(\frac{4}{5}\)

I substituted numbers- 100 total car spots. 1/5 or 20 are empty. 80 numbers are used spots for both compact and non-compact cars. 2/5 are used by compact cars, which means 3/5 are used by non-compact cars. 3/5 of 80 is 48. 48/80 is not 1/2.... where did i go wrong??
_________________

I substituted numbers- 100 total car spots. 1/5 or 20 are empty. 80 numbers are used spots for both compact and non-compact cars. 2/5 are used by compact cars, which means 3/5 are used by non-compact cars. 3/5 of 80 is 48. 48/80 is not 1/2.... where did i go wrong??

The red part is not correct. Total of 100 spots: 20 are empty; 80 are used; 40 are used by compact cars; 80-40=40 are used for non-compact cars.

So non-compact cars take 40/80=1/2 of the filled spaces in the garage.

Re: A parking garage has places for a certain number of cars. If [#permalink]

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23 Aug 2014, 07:26

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A parking garage has places for a certain number of cars. If [#permalink]

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07 Dec 2015, 07:58

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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