Of the applicants passes a certain test, 15

[rakeshd347]

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

OA is D

[theCodeToGMAT]

I tried but i got very strange answer.. what mistake i made

[mevicks]

Given:
20% of x = 15
Thus, x = 75
25% of y = 15
Thus, y = 60

The completed table is


Thus those who applied to only college X or college Y = 60 + 45 = 105

[spoiler]Answer: D[/spoiler]


Regards,
Vivek

[Brent@GMATPrepNow]

I tried but i got very strange answer.. what mistake i made

You almost have it.

If A = total # of people who applied to college X, then 0.2A = 15
Solve to get A = 75
So, 75 people applied to college X

Likewise, if B = total # of people who applied to college Y, then 0.25A = 15
Solve to get B = 60
So, 60 people applied to college Y

etc.

Cheers,
Brent

[mevicks]

I tried but i got very strange answer.. what mistake i made

Hi Rahul,

15 = 20% A + 25% B is the problem.

The statement says If 20 % of the applicants who applied college X applied to both the colleges so you should equate them individually.

Hope that helps.

Regards,
Vivek

[Brent@GMATPrepNow]

Incidentally, if anyone is wondering what the diagrams in mevicks' and theCodeToGMAT's solutions mean, they are using a technique known as the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of applicants, and the two characteristics are:
- applied to college X or didn't apply to college X
- applied to college Y or didn't apply to college Y

To learn more about this technique, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Then try these additional practice questions that can be solved using the Double Matrix Method:
- https://www.beatthegmat.com/mba/2011/05/ ... question-1
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
- https://www.beatthegmat.com/mba/2011/05/ ... question-3
- https://www.beatthegmat.com/ds-quest-t187706.html
- https://www.beatthegmat.com/overlapping- ... 83320.html
- https://www.beatthegmat.com/finance-majo ... 67425.html
- https://www.beatthegmat.com/ds-french-ja ... 22297.html
- https://www.beatthegmat.com/sets-t269449.html#692540
- https://www.beatthegmat.com/in-costume-f ... tml#692116

Cheers,
Brent

[theCodeToGMAT]

I tried but i got very strange answer.. what mistake i made

Hi Rahul,

15 = 20% A + 25% B is the problem.

The statement says If 20 % of the applicants who applied college X applied to both the colleges so you should equate them individually.

Hope that helps.

Regards,
Vivek

Vivek, the question doesn't state the case "individually" very clearly...

If 20 % of the applicants who applied college X and 25% of the applicants who applied college Y applied both college X and Y

There are two ways of interpreting this question: one which I did & other which you did.

[mevicks]

I tried but i got very strange answer.. what mistake i made

Hi Rahul,

15 = 20% A + 25% B is the problem.

The statement says If 20 % of the applicants who applied college X applied to both the colleges so you should equate them individually.

Hope that helps.

Regards,
Vivek

Vivek, the question doesn't state the case "individually" very clearly...

If 20 % of the applicants who applied college X and 25% of the applicants who applied college Y applied both college X and Y

There are two ways of interpreting this question: one which I did & other which you did.

Umm, I think there's only one way of interpreting the wording. However, I might have not explained it correctly so check out Brent's explanation for a detailed one. Let me know if it helps.

Regards,
Vivek

[Brent@GMATPrepNow]

The equation 15 = 20% A + 25% B assumes that there is no overlap. That is, it assumes that no one applied to college X AND to college Y. However, we know that isn't the case. There is definitely overlap.


Here's another way to put it.
Let's say that we have 10 children.
If we're told that 9 children like ice cream and 8 children like apples, we can't then say that 9 + 8 equals the number of children who like both.

Cheers,
Brent

[rakeshd347]

The equation 15 = 20% A + 25% B assumes that there is no overlap. That is, it assumes that no one applied to college X AND to college Y. However, we know that isn't the case. There is definitely overlap.


Here's another way to put it.
Let's say that we have 10 children.
If we're told that 9 children like ice cream and 8 children like apples, we can't then say that 9 + 8 equals the number of children who like both.

Cheers,
Brent

I made the same mistake what Rahul Made. Assuming 20% of A+25% of B=15 and that is where I got stuck. Thanks brent.

[vipulgoyal]

I think the trap is between AND and OR, If it would have been "OR"
If 20 % of the applicants who applied college X OR 25% of the applicants who applied college Y applied both college X and Y , then
4x + 5y = 300
substitute x for 50 and y for 20 such that 20% for 50 and 25 % of 20 equals to 15
now only students for x OR only students for y = 35 + 5 = 40

[telberrak]

"If 20 % of the applicants who applied college X and 25% of the applicants who applied college Y applied both college X and Y"

I personally found the "and" of the statement confusing => 0.2A + 0.25B = 15

[nikhilgmat31]

At first place, we think it as both combines to 15
and makes equation 4x + 5y = 300 which is absolutely wrong.

[Amrabdelnaby]

Hi Brent,

But the question says: If 20 % of the applicants who applied college X and 25% of the applicants who applied college Y applied both college X and Y

so i thought that 20% of X plus 25% of Y equals to 15!

why is this wrong

I tried but i got very strange answer.. what mistake i made

You almost have it.

If A = total # of people who applied to college X, then 0.2A = 15
Solve to get A = 75
So, 75 people applied to college X

Likewise, if B = total # of people who applied to college Y, then 0.25A = 15
Solve to get B = 60
So, 60 people applied to college Y

etc.

Cheers,
Brent

[[email protected]]

Hi amrabdelnaby,

The 20% who applied to college X are the SAME PEOPLE who comprise the 25% who applied to college Y. As such, you CANNOT count them twice.

GMAT assassins aren't born, they're made,
Rich