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

Question

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

(A) 135 
(B) 120 
(C) 115 
(D) 105 
(E) 90

Bunuel · Accepted Answer

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.

Funsho84 · Answer

Set up double matrix

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

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

(75-15) + (60-15) = 105
Answer d

mdali · Answer

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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gmatkillerdude · Answer

Why is the equation not 0.2x+0.25y=15. Isn't the question saying this

pandeyashwin · Answer

it's saying 0.2x = 15 or 0.25y = 15 // 0.2x = 0.25y

ScottTargetTestPrep · Answer

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

mba20202022 · Answer

Bunuel  
I agree that the question stem quite misleads.
I also thought that it is 0.2x+0.25y=15 since it was written " If 20 % of the applicants who applied college X  and  25% of the applicants who applied college Y applied both college X and Y". the *and* part is quite ambiguous.

could you please let me know if I missed anything in the Qs? (when I read the explanations, I easily realized what the right answer was)

VirFortis · Answer

Wow! The question's language is so bad that I had to complain about it in frustration. How can anyone make sense of this?

Once, I saw Bunuel's response, I understood what was being said. I sure do hope, GMAT never does this nasty trick just to make an easy question hair-pullingly frustrating.

This is how the question sounded to me - A sample representation: 10 go to 30 from 50 left. how many go?

I didn't want to just complain so here is a better version of the question :

Of the applicants who passed a certain test, 15 applied to both college X and Y. If 20% of the passing applicants who applied to college X and 25% of the passing applicants who applied to college Y are both equal to the number of passing applicants who applied to both X and Y. How many passing applicants have applied to only college X or college Y?

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

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