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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.

Official Answer is B...

Shouldnt the answer be E...

B is correct!!

Let a and b are the number of students who own and do not own a car resp. We need to find the value of B. Also a+b = 80 Statemen1 : not sufficient.

Statement 2: 42% of a = female => 42a/100 = female = 21a/50.

Now here is the trick !! number of females must be an integer. => a must have minimum value of 50.

if a = 50 => females = 21. a can not be 100 as total is 80

=> a has to be 50. Hence B

The value of 'a' can be zero as well, at least mathematically as that would also justify above conditions. Of course, that makes the statement 2 a tad impractical, but still correct mathematically. So, the value of 'a' can not be ascertained for sure and the answer should still be E.

A bit of an ambiguous question for sure. Maybe the questions needs to mention that a and b are non-zero or something.

It can be 0 and then 42% of the same would also be 0 (number of females). Where does it say in the question that number of females have to be non-zero. All we know is that females = 0.42*a and this equation can be valid at both a = 0 and a = 50 without contradicting anything given in the question.

It can be 0 and then 42% of the same would also be 0 (number of females). Where does it say in the question that number of females have to be non-zero. All we know is that females = 0.42*a and this equation can be valid at both a = 0 and a = 50 without contradicting anything given in the question.

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

The phrase 'Of the students who own a car' already tells you that some students own a car, so it is not a possibility that 0 students own a car. Further, if I were to tell you that 0 people own a car, and I asked you what percentage of the students who own a car are female, you would not say "42%". It would be meaningless to assign a percentage in that case. The GMAT would never tell you '42% of people own a car' and then make the 'trap' that 0 people might own a car, because most test takers would, very reasonably, assume the number of car owners needs to be non-zero.

So if you see a phrase like '1/3 of the people in North America who own a computer are Canadian' or '45% of the marbles in a bag are green', you can certainly assume that the number of North Americans who own a computer, or the number of marbles in the bag, is not zero. _________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Re: In a group of 80 college students, how many own a car? (1) [#permalink]
29 Mar 2014, 10:31

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Re: In a group of 80 college students, how many own a car? [#permalink]
29 Mar 2014, 10:48

Expert's post

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. Clearly insufficient.

(2) Of the students who own a car, 42% are female --> let # of students who own a car be x --> 0.42x= # of females who own a car. But 0.42x must be an integer, as it represent # of females. 0.42x=integer --> \frac{21}{50}x=integer --> x is a multiple of 50: 50, 100, 150, ... But x (# of students who own car) must also be less than (or equal to) 80. So x=50. sufficient.

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