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cano
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JJ2014
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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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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cano
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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So assume total slots 25

Empty- 5
Compact - 10
Non compact- 10

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

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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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I keep thinking that the 2/5 are of the filled space so 2/5 * 4/5 = compact car filled parking lots. Any tips on how to understand the prompt better?
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cano
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. \(\frac{4}{5}\)

I keep thinking that the 2/5 are of the filled space so 2/5 * 4/5 = compact car filled parking lots. Any tips on how to understand the prompt better?

Assume there are 5 parking spaces:

  • 1 space is empty.
  • 2 spaces are used by compact cars.
  • The remaining 2 spaces are used by non-compact cars.

In total, 4 spaces are filled. Non-compact cars occupy 2 of these, making the fraction of filled spaces they take up 2 out of 4, or 1/2.
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hey Bunuel , let total be n and then empty are 1/5n and then 4/5 are filled . in those filled 2/5 are compact then that means 2/5 into 4/5 which is 8/25n so now remaining space is 12/25n and ans is 12/25/4/5 which comes out as 3/5 what did i do wrong please explain boss please!!
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cano
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. \(\frac{4}{5}\)

hey Bunuel , let total be n and then empty are 1/5n and then 4/5 are filled . in those filled 2/5 are compact then that means 2/5 into 4/5 which is 8/25n so now remaining space is 12/25n and ans is 12/25/4/5 which comes out as 3/5 what did i do wrong please explain boss please!!

The red part is not correct.

As \(\frac{n}{5}\) of the places are left empty, then \(\frac{4n}{5}\) of the places are filled.

Out of these, \(\frac{2n}{5}\) of the places are used by compact cars, so \(\frac{4n}{5}-\frac{2n}{5}=\frac{2}{5}\) are used by non-compact cars.

This means that non-compact cars take \(\frac{(\frac{2n}{5})}{(\frac{4n}{5})}=\frac{1}{2}\) of the filled spaces in the garage.

Alternatively, pick a smart number for the total places, such as 5. If 1 place is left empty, then 4 places are used. Of these, 2 places are used by compact cars and 2 by non-compact cars. Therefore, non-compact cars take \(\frac{2}{4}=\frac{1}{2}\) of the filled spaces in the garage.

Answer: C.

P.S. When facing problems, with your approach, please review the solutions provided carefully. They might give you a hint about where you are going wrong with your approach.
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