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

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Of the applicants passes a certain test, 15 applied to both college X  [#permalink]

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New post 07 Apr 2018, 14:27
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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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Re: Of the applicants passes a certain test, 15 applied to both college X  [#permalink]

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New post 07 Apr 2018, 14:27
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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: \(60+45=105\).

Answer: D.
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Re: Of the applicants passes a certain test, 15 applied to both college X  [#permalink]

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New post 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
Answer d
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Re: Of the applicants passes a certain test, 15 applied to both college X  [#permalink]

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New post 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  [#permalink]

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New post 16 Oct 2018, 10:24
Why is the equation not 0.2x+0.25y=15. Isn't the question saying this
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Of the applicants passes a certain test, 15 applied to both college X  [#permalink]

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New post 17 Oct 2018, 06:43
gmatkillerdude wrote:
Why is the equation not 0.2x+0.25y=15. Isn't the question saying this

it's saying 0.2x = 15 or 0.25y = 15 // 0.2x = 0.25y
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Re: Of the applicants passes a certain test, 15 applied to both college X  [#permalink]

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New post 17 Oct 2018, 19:02
Letting x = the number of applicants who applied to college X and y = the number of applicants who applied to college Y, we have:

0.2x = 15 and 0.25y = 15

So x = 75 and y = 60. We can use the following formula to determine the total number of applicants:

Total = College X + Collge Y - Both colleges

Total = 75 + 60 - 15

Total = 120

Since 15 of 120 applicants applied to both colleges, then 120 - 15 = 105 applicants applied to either college (but not both).

Answer: D
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Re: Of the applicants passes a certain test, 15 applied to both college X &nbs [#permalink] 17 Oct 2018, 19:02
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