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Of all students in a certain dormitory, 1/2 are first-year

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Of all students in a certain dormitory, 1/2 are first-year

by AAPL » Wed Jun 06, 2018 4:32 am

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Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 3 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?

A. 1/15
B. 1/5
C. 4/15
D. 1/3
E. 2/5

The OA is B.

100 Students Total:

1st yr = 50 students
4/5x50 = 40 = No Major
Therefore: 10 = Major

2nd yr = 50 students
10x3 = 30 = Major
Therefore: 20 = No Major
20/100 = 1/5 = B.

Has anyone another strategic approach to solve this PS question? Regards!
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by swerve » Wed Jun 06, 2018 10:01 am
Total students = x

1st year student = x/2 --> non major = 4/5(x/2) --> major = 1/5(x/2)
2nd year student = x/2 --> major = 3(1/5(x/2)) = 3/10(x) = --> non major = x/2 - 3/10(x) = 1/5(x)

Hence B is the correct answer. Regards!
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by Scott@TargetTestPrep » Thu Jun 07, 2018 4:14 pm
AAPL wrote:Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 3 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?

A. 1/15
B. 1/5
C. 4/15
D. 1/3
E. 2/5
Since 1/2 are first-year students, the other 1/2 are second-year students. Since 4/5 of the first-year students have not declared a major, so 1/5 of them have declared a major. Since the fraction of second-year students who have declared a major is 3 times the fraction of first-year students who have declared a major, 3/5 of the second-year students have declared a major. Therefore, 2/5 of the second-year students have not declared a major. Since the second-year students are 1/2 of all the students, 1/2 x 2/5 = 1/5 of all students are second-year students who have not declared a major.

Answer: B

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