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Of the applicants passes a certain test, 15 applied to both college X

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Math Expert
Joined: 02 Sep 2009
Posts: 47183
Of the applicants passes a certain test, 15 applied to both college X  [#permalink]

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07 Apr 2018, 14:27
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Difficulty:

55% (hard)

Question Stats:

60% (01:29) correct 40% (02:48) wrong based on 82 sessions

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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

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Math Expert
Joined: 02 Sep 2009
Posts: 47183
Re: Of the applicants passes a certain test, 15 applied to both college X  [#permalink]

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07 Apr 2018, 14:27
Bunuel 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

Question means the following:
15 people applied to both college X and Y, these 15 people represent 20% of all applicants who applied to X and 25% of all applicants who applied to Y.

$$0.2*x=15$$ --> $$x=75$$ --> # of people who applied only to X is: $$75-15=60$$;
$$0.25*y=15$$ --> $$y=60$$ --> # of people who applied only to Y is: $$60-15=45$$;

# of people who applied only to X OR Y is: $$60+45=105$$.

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Joined: 08 Sep 2016
Posts: 116
Re: Of the applicants passes a certain test, 15 applied to both college X  [#permalink]

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07 Apr 2018, 14:38
Set up double matrix

(1/4)*y = 15
y=60

(1/5)*x = 15
x= 75

(75-15) + (60-15) = 105
Intern
Joined: 03 Oct 2015
Posts: 1
Re: Of the applicants passes a certain test, 15 applied to both college X  [#permalink]

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13 Apr 2018, 10:21
in x
when both is 20 then x= 100
15. 100*15/20
=75
only x = 60
likely
y= 60
only y = 45
so only x and y = 60+45
=105

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Re: Of the applicants passes a certain test, 15 applied to both college X &nbs [#permalink] 13 Apr 2018, 10:21
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