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.
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ajith
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Say , there x number students in the schoolmgmt_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.
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
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onedayi'll
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komal
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A confusing one for sure. Here's a very neat explanation i found. Hope it helps : )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.
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.
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Jeff@TargetTestPrep
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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: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.
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
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