A parking garage has places for a certain number of cars. If : GMAT Problem Solving (PS)
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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]

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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. $$\frac{4}{5}$$
[Reveal] Spoiler: OA
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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.

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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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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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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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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]

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13 Nov 2012, 06:03
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Re: A parking garage has places for a certain number of cars. If [#permalink]

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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
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23 Aug 2014, 06:26
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07 Dec 2015, 06:58
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Re: A parking garage has places for a certain number of cars. If [#permalink]

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28 Dec 2015, 11:58
What is important is to read the question properly. The questions asks for fraction of filled spaces and not the total parking space

Let total parking space be 100%

1/5 th is empty = 20% is empty

2/5th = compact cars = 40%

Non compact cars = 40%

Total filled up = 80%

Non compact cars occupies half of the filled spaces. Hence, 50% or 1/2
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Re: A parking garage has places for a certain number of cars. If   [#permalink] 28 Dec 2015, 11:58
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