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

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cano
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A parking garage has places for a certain number of cars. If [#permalink] New post   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. \(\frac{4}{5}\)
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C
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Bunuel
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Re: A parking garage has places for a certain number of cars. If [#permalink] New post   17 Sep 2010, 01:14
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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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JJ2014
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Re: A parking garage has places for a certain number of cars. If [#permalink] New post   12 Nov 2012, 12:44
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: A parking garage has places for a certain number of cars. If [#permalink] New post   13 Nov 2012, 03:05
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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   24 May 2013, 20:52
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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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Re: A parking garage has places for a certain number of cars. If [#permalink] New post   13 Feb 2018, 17:59
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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. \(\frac{4}{5}\)


Let’s say there are a total of 50 places in the parking garage.

Since 1/5 of the places are empty, 4/5 x 50 = 40 are being used.

Since 2/5 of the places are taken up by compact cars, 2/5 x 50 = 20 places are taken up by compact cars. Thus we must have 40 - 20 = 20 places that are taken up by non-compact cars

So, 20/40 = 1/2 of the spots are taken up by non-compact cars.

Answer: C
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Re: A parking garage has places for a certain number of cars. If 1/5 of th [#permalink] New post   06 May 2019, 21:17
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So assume total slots 25

Empty- 5
Compact - 10
Non compact- 10

Ratio - 10/ (10+10)= 1/2

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Re: A parking garage has places for a certain number of cars. If 1/5 of th [#permalink] New post   07 May 2019, 21:58
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Empty space=1/5
Filled space in parking=1-(1/5)=4/5
Space compact car takes= 2/5
Space taken up by non compact car= 4/5 - 2/5= 2/5
Fraction of space non compact car takes of filled space= (2/5)÷(4/5)= 1/2
IMO C

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Re: A parking garage has places for a certain number of cars. If [#permalink] New post   21 Sep 2020, 06:14
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Re: A parking garage has places for a certain number of cars. If [#permalink]
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