Of the students in a certain school, 65 percent are enrolled in an art

Question

Of the students in a certain school, 65 percent are enrolled in an art class and 70 percent are enrolled in a music class. What percent of the students in the school are enrolled in both an art class and a music class?

(1) 25 percent of the students are enrolled in only a music class.

(2) The ratio of the number of students who are enrolled in both an art class and a music class to the number of students who are enrolled in neither an art class nor a music class is 9 to 2.

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Purnank · Answer

lets assume total as 100x.
1st - both = 70x-25x = 45x
Sufficient
2nd - Talks about ratio to both to none = 9:2

65x+70x-both+none = 100x

135x-9k+2k=100x

7k = 35x

k=5x

Therefore, both = percent of the students in the school are enrolled in both an art class and a music class  = 9k = 45x =  45%
Sufficient.
  Answer is D.

TheVDR · Answer

4 categories of students :

(Music Class with Art Class); (Music Class without Art Class); (Art Class without Music Class); (Neither Art Class nor Music Class)

Statement (1)   
Music Class (Total) = (Music Class with Art Class) + (Music Class without Art Class)
70% = (Music Class with Art Class) + 25%

Sufficient

Statement (2)  
(Music Class with Art Class) : (Neither Art Class nor Music Class) = 9 : 2.......(Equation 1)

Now, Art Class (Total) = 65%
Thus, 100 - 65 = 35% do not attend art class.

35 - (Neither Art Class nor Music Class) = (Music Class without Art Class).......(Equation 2)

Also, Music Class (Total) = 70%

70 - (Music Class with Art Class) = (Music Class without Art Class).......(Equation 3)

We have 3 unique equations and 3 variables, one of which is asked by the question.

Sufficient

PS : Just in case you are curious, here are the percentages :

(Art with Music) = 45%
(Art without Music) = 20%
(Music without Art) = 25%
(Neither) = 10%

Pranavsawant · Answer

No no no no!!!!

1) 70 percent are enrolled in a music class
2) 25 percent of the students are enrolled in only a music class.

From these two statements we can conclude that 45% of the students are not enrolled in only a music class. This could be music + art, music + sport, music + french or whatever. We can't conclude from this that music + art is 45%

All that we can really say from the prompt is that the intersection (Both music and art) will be in the range   
And from the reasoning above, we now know that the new upper bound is 45%

So all we know that music and art is in the range   (expressed in %)
We don't know it's exact value.

Pranavsawant · Answer

Yo yo yo yo yo!!! Statement 1 says people who take only music is 25% You are saying people who take music and don't take art = 25% But those two aren't the same!!!! In general, people who take only music != people who take music and don't take art. People who take music and don't take art could be larger than the people who take only music. Consider the case of a student who takes music and geography. He doesn't come under the 25% that take only music but does come under the set of people who take music and don't take art. So when you say that people who take only music (as said in statement 1) = people who take music and not art = 25%, that's a mistake

TLDR: You're making the assumption that people who don't take music are auto-enrolled in art. In that case, yes music and art would be 45%. But we can't make that assumption. The prompt never says a given student has to take from one of music/art

anshumanmalliwal · Answer

I have doubt in the solution of statement 1, we are given that "25 percent of the students are enrolled in only a music class", but how can we infer that remaining all are in art class as well. We are not told that these two are the only subjects. what if 20% students enrolled in music and say maths.

How can we be sure that 45% are in both art and music class?

How can we be sure that 45% are in both art and music class?

Of the students in a certain school, 65 percent are enrolled in an art

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GMAT Data Sufficiency (DS) Questions

Of the students in a certain school, 65 percent are enrolled in an art

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

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Perfect 805 Score Debrief by Julia

My Rewards