Sample of College Students

[TxGMAT]

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.

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Hi TxGMAT,

You can solve this question algebraically or by TESTing VALUES (although you will have to stay organized regardless of which approach you use). Based on what we told...

IF... there are 100 total students
then 40 of those students are third-year students
and 70 of those students are NOT second-year students.

By extension, 40 of those 70 students who are NOT second-year students are already accounted for (they're the 40 third-year students), so there are 30 OTHER students in that group of 70. So far, we've accounted for 70 of the 100 total students, which means that there are 30 additional students who must be second-year students.

Thus, we have....
30 second-year students
40 third-years students
30 additional students who are NOT second-year students (maybe they're first-year or fourth-year, but they are NOT second-year nor third-year).

The question asks for the fraction of students out of those who are NOT third-years, but are second-years...

Total NOT third-years = 60 students
Total second-years = 30 students

30/60 = 1/2

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[Jay@ManhattanReview]

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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[Scott@TargetTestPrep]

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

We can let the total number of students be 100. Since 40% are third-year students, 40 students are third-year. Thus, 60 students are not third-year. Since 70% are not second-year, 70 students are not second-year. Thus, 100 - 70 = 30 students are second-year.

Since 60 students are not third-year and 30 students are second-year, the fraction of students who are not third-year but are second-year is:

30/60 = 1/2

Answer: D