TxGMAT wrote:In a sample of college students, 40 percent are third-year students and 70 percent are NOT second-year students. What fraction of those students who are not third year students are second-year students?
A) 3/4
B) 2/3
C) 4/7
D) 1/2
E) 3/7
I know that A through C are incorrect, but I can't get to the bottom of why the answer is 3/7. I knew in my gut but I couldn't work it out. Please help.
Hi TxGMAT,
We do not know whether the situation being discussed is for a 3-, 4- or 5-year degree students; however, this is not needed to reach the answer.
We want:
The ratio of # of second-year students / # of students who are not third-year students
We know that the % of third-year students = 40% => # of students who are not third-year students = 100 - 40 = 60% (the denominator)
Again, # of students who are not second-year students = 70% => # of second-year students = 100 - 70 = 30% (numerator)
The required ratio = # of second-year students / # of students who are not third-year students = 30% / 60% = [spoiler]1 : 2[/spoiler].
The correct answer:
D
Hope this helps!
Relevant book:
Manhattan Review GMAT Word Problems Guide
-Jay
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