Of the K vehicles parked in a certain parking lot, 0.125k are vans.

Question

Of the K vehicles parked in a certain parking lot, 0.125k are vans. Of the remaining vehicles, 1/7 are midsize cars and the rest are compact cars. What percent of the vehicles parked in the parking lot are compact cars?

A) 50%
B) 73.2%
C) 75%
D) 85.7%
E) 90%

A. 50%
B. 73.2%
C. 75%
D. 85.7%
E. 90%

gmatophobia · Accepted Answer

Assume number of cars = x

0.125 =  \frac{1}{8}

Out of k parked vehicles,  \frac{x}{8} th are vans.

Remaining vehicles =  1-\frac{1}{8} = \frac{7x}{8}

Of the remaining vehicles, 1/7 are midsize cars   ⇒

Mid Size Cars =  \frac{1}{7} * \frac{7}{8} = \frac{x}{8}

Remaining cars =  \frac{6x}{8}

Percentage =  \frac{6x}{8x}/x * 100

=  \frac{6}{8}* 100  = 75%

Option C

Kinshook · Answer

Given: Of the K vehicles parked in a certain parking lot, 0.125k are vans. Of the remaining vehicles, 1/7 are midsize cars and the rest are compact cars.

Asked: What percent of the vehicles parked in the parking lot are compact cars?

Total vehicles = K
Vans = .125K = K/8
Remaining vehicles = K - .125K = .875K = 7K/8
Midsize cars = (7K/8)/7 = K/8
Compact cars = 7K/8 - K/8 = 6K/8 = 3K/4

The percent of the vehicles parked in the parking lot that are compact cars = (3K/4)/K * 100% = 75%

IMO C

Abhishek009 · Answer

0.125  must ring the bells that  0.125=\frac{1}{8}

Let, there be  8  vehicles or  k = 8

No of Vans  = 1  ; remaining Vehicles  = 7

Thus, mid sized cars  = 1  ; remaining cars (compact cars)  = 6

Thus, % compact cars is  \frac{6}{8}*100 = 75 , Answer must be (C)

JeffTargetTestPrep · Answer

Since 0.125 = 1/8, the number of vans is (1/8)k, and the number of remaining vehicles is (7/8)k.

total vehicles = vans + midsize cars + compact cars

k = (1/8)k + (1/7)(7/8)k + (6/7)(7/8)k

Therefore,

compact cars = (6/7)(7/8)k = (6/8)k = (3/4)k

We see that 3/4, or 75%, of the total vehicles are compact cars.

Answer: C

DanTheGMATMan · Answer

This problem is a total overlapping sets head fake. Really just a word problem:

https://www.youtube.com/watch?v=gj5Q48qmIjk

bumpbot · Answer

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Of the K vehicles parked in a certain parking lot, 0.125k are vans.

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Of the K vehicles parked in a certain parking lot, 0.125k are vans.

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