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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
[Reveal] Spoiler: OA

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Expert Post
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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
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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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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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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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] 13 Apr 2018, 10:21
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