Need help with this wordy GMAT question on student majors and fractions.?
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
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
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Asked by M Rizwan 25 days ago
This one's classic GMAT — lots of fractions but manageable if you break it into chunks.
• Total students = T
• First-year = 0.5T → 4/5 haven’t declared major = 0.4T
• So declared majors among first-years = 0.1T
• Declared majors among second-years = 3 × 0.1T = 0.3T
• Second-year total = 0.5T → not declared = 0.5T – 0.3T = 0.2T
• So second-years with no major = 0.2T out of T total students = 0.2 = 1/5
Answer is B. All the values fall into place once you assign T and break the info into parts
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