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onesome: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Fri May 23, 2008 6:45 am

PS - sets question - tricky

by onesome » Sun Jul 06, 2008 2:38 pm

Of the applicants passes a certain test, 15 applied to both college X and Y. If 20 % of the applicants who applied college X and 25% of the applicants who applied college Y applied both college X and Y, how many applicants applied only college X or college Y?
A) 135
B) 120
C) 115
D) 105
E) 90

Answer is : D

Please suggest how to solve this question.
Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Sun Jul 06, 2008 2:38 pm

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

Re: PS - sets question - tricky

by Stuart@KaplanGMAT » Sun Jul 06, 2008 6:43 pm

onesome wrote:Of the applicants passes a certain test, 15 applied to both college X and Y. If 20 % of the applicants who applied college X and 25% of the applicants who applied college Y applied both college X and Y, how many applicants applied only college X or college Y?
A) 135
B) 120
C) 115
D) 105
E) 90

Answer is : D

Please suggest how to solve this question.
Thanks in advance.

15 people applied to both college X and Y, and we know that number represents 20% of all applicants to X and 25% of all applicants to Y.

So:

1/5(x) = 15
x = 75

1/4(y) = 15
y = 60

We want to know how many people didn't apply to BOTH colleges (i.e. how many applied to only 1 college).

Of the 75 people who applied to X, 15 applied to both, so:

75-15 = 60 applied only to X

Of the 60 people who applied to Y, 15 applied to both, so:

60 - 15 = 45 applied only to Y.

60 + 45 = 105: choose (D).