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A parking garage has spaces for cars and vans only. If there

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A parking garage has spaces for cars and vans only. If there

by BTGmoderatorDC » Sun Apr 28, 2019 7:21 pm

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A parking garage has spaces for cars and vans only. If there is a total of 118 vehicles in the garage, how many of them are vans?

(1) If 14 more vans are driven into the garage, there will be twice as many vans as cars in the garage.

(2) If x vans and y cars are driven into the garage, there will be an equal number of vans and cars in the garage.


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Source: Princeton Review
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Source: — Data Sufficiency |
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by deloitte247 » Fri May 03, 2019 6:28 am

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$$Let\ the\ number\ of\ Vans\ =\ x$$
$$Let\ the\ number\ of\ Cars\ =\ y$$
$$x+y=118\ $$
The question now is How many of them are Vans? (i.e. What is the value of x)
Statement 1:- If 14 more Vans are driven into the garage, there will be twice Vans as Cars in the garage.
$$So,\ y=\frac{\left(x+14\right)}{2}$$
$$x+y=118\ \ \ \left(sub.\ the\ new\ value\ of\ y\right)$$
$$\left(x+14\right)+\frac{\left(x+14\right)}{2}=118+14=132$$
$$\frac{\left(2x+28+x+14\right)}{2}=132$$
$$2x+28+x+14=264$$
$$3x=222$$
$$x=\frac{222}{3}=74$$
$$Thus,\ Statement\ 1\ is\ SUFFICIENT$$

Statement 2:- If x Vans and y Cars are driven into the garage, there will be equal number of Vans and Cars in the garage.
The value of x Vans and y Cars that were driven into the garage is unknown.
$$Hence,\ statement\ 2\ is\ NOT\ SUFFICIENT$$
$$In\ conclusion,\ Statement\ 1\ alone\ is\ SUFFICIENT\ ,\ thereby\ validating\ OPTION\ A\ as\ the\ correct\ answer.$$
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