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505-555 (Easy)|   Fractions and Ratios|   Overlapping Sets|                           
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I was confused between 1/5 and 2/5 ,how to know whether they want the total from the whole set of students or just the second year ones?
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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

Answer: Option B

Video solution by GMATinsight

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ImChasmish

It was mentioned in the last line "what fraction of all the students in the dormitory are second-year students who have not declared a major?
What fraction from all the students = Total students (denominator), so fraction is out of all the students (first + second year)
second-year students who have not declared a major - Numerator

ImChasmish
I was confused between 1/5 and 2/5 ,how to know whether they want the total from the whole set of students or just the second year ones?
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Solution:
• 1/2 are first-year, 1/2 are second-year.
• 4/5 of first-years have not declared, so 1/5 of first-year have.
• 3/5 of second-years have declared, so 2/5 of second-year have not.
The fraction of all students who are second-years and have not declared is:
1/2×2/5=1/5
Final Answer:
(B) 1/5
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