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

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VP
Joined: 09 Jul 2007
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Of the students in a certain school, 15 percent are enrolled [#permalink]

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07 Dec 2007, 18:54
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

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Manager
Joined: 04 Nov 2007
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07 Dec 2007, 21:01
Ravshonbek 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

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

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Senior Manager
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07 Jun 2008, 14:02
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?

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Director
Joined: 14 Oct 2007
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Location: Oxford
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07 Jun 2008, 14:20
mbawaters wrote:
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?

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

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Senior Manager
Joined: 12 Apr 2008
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Location: Eastern Europe
Schools: Oxford

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07 Jun 2008, 14:22
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.

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Current Student
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07 Jun 2008, 18:55
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

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Director
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08 Jun 2008, 23:55
mbawaters wrote:
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?

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

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

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VP
Joined: 18 May 2008
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09 Jun 2008, 00:07
I prefer to use the following method:
Total=A+B-Both+Neither
(1) is telling Neither
Sufficient

Last edited by ritula on 09 Jun 2008, 03:22, edited 1 time in total.

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Manager
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09 Jun 2008, 00:29
The answer is A. I would recommend looking up set theory and venn diagrams, which will help immediately clarify questions such as this.

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Re: SET   [#permalink] 09 Jun 2008, 00:29
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# Of the students in a certain school, 15 percent are enrolled

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