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02 Aug 2024, 01:31
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
59% (02:01) correct
41%
(02:18)
wrong
based on 203
sessions
History
Date
Time
Result
Not Attempted Yet
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.
(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.
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.
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.
03 Aug 2024, 06:32
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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%
(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%
