All AnswersNeed help with this wordy GMAT question on student majors and fractions.?
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
Asked by M Rizwan 25 days ago
Seo Executive
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
Detail-Oriented Financial Analyst
Looks messy at first, but it’s actually just a layered fractions problem. Start by assuming total students = T. Since half are first-years, both first-year and second-year totals = 0.5T.
Out of the first-years, 4/5 haven’t declared a major. So 0.5T × 4/5 = 0.4T haven’t declared, meaning 0.1T have declared.
Now, the declared majors among second-years is 3 times that → 3 × 0.1T = 0.3T.
So among second-years:
Declared = 0.3T
Total = 0.5T
So not declared = 0.5T – 0.3T = 0.2T
Now find the fraction of all students that are second-years with no major:
That’s 0.2T / T = 1/5
Final answer: B
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