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In a group of 80 college students, how many own a car?

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Source: — Data Sufficiency |
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by AAPL » Fri Nov 15, 2019 4:23 am
BTGmoderatorDC wrote:In a group of 80 college students, how many own a car?

(1) Of the students who do not own a car, 14 are male.
(2) Of the students who own a car, 42% are female.

OA B

Source: Magoosh
1) Of the students who do not own a car, 14 are male. Clearly insufficient. \(\Large{\color{red}\chi}\)

2) Of the students who own a car, 42% are female.

\(\Rightarrow\) let \(\#\) of students who own a car be \(x \Rightarrow 0.42x=\#\) of females who own a car. But \(0.42x\) must be an integer, as it represents \(\#\) of females. \(0.42x =\) integer \(\Rightarrow \frac{21}{50}x=\) integer \(\Rightarrow\, x\) is a multiple of \(50: 50, 100, 150, \cdots\). But \(x\) (\(\#\) of students who own car) must also be less than (or equal to) \(80\). So \(x=50\). Sufficient. \(\Large{\color{green}\checkmark}\)

Therefore, __B__
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