Of the students in a certain school, 15 percent are enrolled

Question

Of the students in a certain school, 15 percent are enrolled in an art class and 10 percent are enrolled in a music class. What percent of the students in the school are enrolled in neither an art class nor a music class?

(1) 2/3 of the students who are enrolled in an art class are also enrolled in a music class.
(2) There are more than 100 students in the school.

 A

tnguyen707 · Answer

a. 2/3 of 15% of total students who are enrolled in Art = 10% of total students are enrolled in art and also in music (both). That leaves 5% only in art. We also know that 10 percent of total students are enrolled in music. That means all students who are enrolled in music must also be in art class. There is no student who study music alone. Thus the total who study art only, and both are 5% + 10% = 15%. That leaves 85% of total students study neither art nor music. Sufficient.

b. Information given is useless to determine the percentage of students who are enrolled in neither. Insuff

Ans = A

mbawaters · Answer

E?
I understand the OA is A but What if we have other students enrolled in subjects other than art & music?

What from the question telling is that there are only these two subjects?

buffdaddy · Answer

Hi MBAWaters,
the students enrolled in the other subjects will simply go in the "not enrolled in either music or art" category

one simple way to solve these type of questions is using a 2d matrix (my preferred method).

let me know if you want me to explain this method

-buff

greenoak · Answer

I don't think there's a problem with the other classes. The question asks specifically for those who were neither in music nor arts. The answer is still A and explanation still works no matter how many other subjects are there.

FN · Answer

the way i do this is as this...

total=Arts+Music-both+Neither..

100%=15+10-10=15...

Neither will have to be 85%..A is sufficient

buffdaddy · Answer

hi All,

a couple of people have asked me how this is solved with a 2d matrix.

below is how i normally do these type of questions

Of the students in a certain school, 15 percent are enrolled in an art class and 10 percent are enrolled in a music class. What percent of the students in the school are enrolled in neither an art class nor a music class?

the matrix looks like
 \begin
\begin{tabular}{|l|l|l|l|}\hline
 & Art & not Art & total \ \hline
Music & & &10%\ \hline
not Music & &x \ \hline
total &15% & &100% \ \hline
\end{tabular}

for the statements:
(1) 2/3 of the students who are enrolled in an art class are also enrolled in a music class.

\begin
\begin{tabular}{|l|l|l|l|}\hline
 & Art & not Art & total \ \hline
Music &\frac{2}{3} * 15 = 10%& 0 &10%\ \hline
not Music & &x = 100-15 = 85% \ \hline
total &15% & 100-15 = 85% &100% \ \hline
\end{tabular}

from the above it can be deduced that x = 85%

(2) There are more than 100 students in the school.

\begin
\begin{tabular}{|l|l|l|l|}\hline
 & Art & no Art & total \ \hline
Music & & &10%\ \hline
not Music & &x \ \hline
total &15% & &100% > 100 students \ \hline
\end{tabular}

from statement 2) we get no additional information that is useful

therefore A

hope that helps

-buff

ritula · Answer

I prefer to use the following method:
Total=A+B-Both+Neither
(1) is telling Neither
Sufficient
A should be the answer

snoor · Answer

The answer is A. I would recommend looking up set theory and venn diagrams, which will help immediately clarify questions such as this.

Of the students in a certain school, 15 percent are enrolled

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