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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: 50000
Of the applicants passes a certain test, 15 applied to both college X  [#permalink]

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07 Apr 2018, 14:27
00:00

Difficulty:

55% (hard)

Question Stats:

64% (01:31) correct 36% (02:26) wrong based on 136 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: 50000
Re: Of the applicants passes a certain test, 15 applied to both college X  [#permalink]

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07 Apr 2018, 14:27
1
1
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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Manager
Joined: 08 Sep 2016
Posts: 118
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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Joined: 10 Dec 2017
Posts: 15
Location: India
Concentration: Entrepreneurship, Social Entrepreneurship
GMAT 1: 710 Q48 V42
GPA: 3.41
Re: Of the applicants passes a certain test, 15 applied to both college X  [#permalink]

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16 Oct 2018, 10:24
Why is the equation not 0.2x+0.25y=15. Isn't the question saying this
Manager
Joined: 14 Jun 2018
Posts: 112
Of the applicants passes a certain test, 15 applied to both college X  [#permalink]

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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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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).

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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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