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A parking garage has places for a certain number of cars. If

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A parking garage has places for a certain number of cars. If [#permalink] New post 17 Sep 2010, 00:05
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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}
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Re: Parking garage [#permalink] New post 17 Sep 2010, 00:14
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cano wrote:
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.

Answer: C.

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Re: Parking garage [#permalink] New post 17 Sep 2010, 00:21
cano wrote:
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}

=\frac{1}{2} , Hence C

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Re: Parking garage [#permalink] New post 17 Sep 2010, 01:28
filled = 1/5
empty = 4/5
compact is = 2/5
non compact is = 4/5 - 2/5 = 2/5
fraction of filled places = 2/5 / 4/5 = 1/2
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Re: Parking garage [#permalink] New post 12 Nov 2012, 11:44
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??

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Re: Parking garage [#permalink] New post 13 Nov 2012, 02:05
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JJ2014 wrote:
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.

Hope it's clear.

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Re: A parking garage has places for a certain number of cars. If [#permalink] New post 13 Nov 2012, 06:03
thanks! i misread the question..

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Re: A parking garage has places for a certain number of cars. If [#permalink] New post 24 May 2013, 19:52
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A visual solution...

[ Empty ] [ Compact ] [ Compact ] [ Non-Compact ] [ Non-Compact ]

Filled spaces = 4
Thus, Non-Compact/Filled spaces = 2/4 = 1/2
Re: A parking garage has places for a certain number of cars. If   [#permalink] 24 May 2013, 19:52
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