mgmt_gmat wrote: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.

Say , there x number students in the school

0.15 x is enrolled for art class
0.10 x is enrolled for music class

1) 2/3 of 0.15x is enrolled in music class and art class
2/3*0.15x = .10x is enrolled in both classes

no of people enrolled neither in art nor in music class =x- ( 0.15+0.10x- 0.10x) = x- 0.15x = 0.85x or 85%
sufficient

2) not sufficient

A is the answer

Agreed with A.

mgmt_gmat wrote: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 confusing one for sure. Here's a very neat explanation i found. Hope it helps : )

Using a Venn Diagram :

Left circle = Art @ 15%. right circle = Music at 10%

(1) tells us 2/3 of the students who are enrolled in an art class (10% of total Population) are also enrolled in a music class. This means that the all of students enrolled in music are also enrolled in an art class. Sufficient.

(2) Doesn't tell us anything about the relationship between the 2 classes. Insufficient.

mgmt_gmat wrote: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.

We can let the total number of students = n, so we have 0.15n students in art class and 0.1n students in music class. We can also use the following the equation:

n = 0.15n + 0.1n - both + neither

n = 0.25n - both + neither

0.75n = neither - both

Notice that we need to determine "neither". We see that if we know "both" in terms of n, then we can determine "neither" in terms of n and, hence, "neither" as a percentage of n, the total number of students in the school.

Statement One Alone:

2/3 of the students who are enrolled in an art class are also enrolled in a music class.

Thus, we know that 2/3(0.15n) = 0.1n both, so we have:

0.75n = neither - 0.1n

0.85n = neither

Thus "neither" is 0.85n/n = 0.85 = 85% of the total number of students.

Statement one alone is sufficient to answer the question.

Statement Two Alone:

There are more than 100 students in the school.

Statement two does not provide enough information to answer the question.

Answer: A