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There are 68 cars on a parking lot. If 36 of the cars are sedans, and

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Bunuel
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There are 68 cars on a parking lot. If 36 of the cars are sedans, and [#permalink] New post   14 Mar 2022, 07:03
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There are 68 cars on a parking lot. If 36 of the cars are sedans, and 48 of the cars have automatic transmissions, what is the ratio of the minimum possible number of sedans with automatic transmissions to the number of cars in the parking lot?

A. 3:17
B. 4:17
C. 5:17
D. 6:17
E. 4:19
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B
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vijayram2496
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Re: There are 68 cars on a parking lot. If 36 of the cars are sedans, and [#permalink] New post   14 Mar 2022, 07:34
Min number of cars with Sedan = 16
Total = 68
Ratio = 4/17

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Re: There are 68 cars on a parking lot. If 36 of the cars are sedans, and [#permalink] New post   14 Mar 2022, 08:22
We need to get the ratio of number of sedans with automatic transmissions to the number of cars in the parking lot

the number of sedans with automatic transmissions is shown in the image with orange colour.

To get the minimum value, we need the number of manual sedan cars to be maximum.
To get the maximum value for manual sedan cars, we need to make manual non-sedan cars to be minimum. Thus if we give 0 to manual non-sedan cars.

Then Automatic Sedan cars = 36 - 20 = 16

Then ratio = 16:68 = 4:17

Answer B
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zoey09
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Re: There are 68 cars on a parking lot. If 36 of the cars are sedans, and [#permalink] New post   21 Dec 2022, 08:47
Here's my 2 cents on this:
1. to have min #sedans with AT => you need to max #sedans with no AT.
2. Total No AT cars = Total - #AT cars = 20 => all of these should be sedans
3. Then you have your min #sedans with AT = 36-20 = 16
4. Your min ratio = 16/68 = 4/17
Hope it is clear and helpful ;)
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Re: There are 68 cars on a parking lot. If 36 of the cars are sedans, and [#permalink] New post   21 Dec 2022, 12:01
Expert Reply
Bunuel wrote:
There are 68 cars on a parking lot. If 36 of the cars are sedans, and 48 of the cars have automatic transmissions, what is the ratio of the minimum possible number of sedans with automatic transmissions to the number of cars in the parking lot?

A. 3:17
B. 4:17
C. 5:17
D. 6:17
E. 4:19


We can create the equation:

68 = 36 + 48 - both + neither

We need to minimize “both.”

SImplifying we have:

68 = 84 - both + neither

Both - neither = 16

So to minimize “both,” we make neither 0, so both = 16.

Thus, the ratio is:

16/68 = 8/34 = 4/17

Answer: B
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Re: There are 68 cars on a parking lot. If 36 of the cars are sedans, and [#permalink]
21 Dec 2022, 12:01
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