prep question

[jamesk486]

In a sample of college students, 40% are third-year students and 70% 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

[jayhawk2001]

In a sample of college students, 40% are third-year students and 70% 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

Without knowing how many years are there in total, it is hard to
determine the answer.

If we assume just 3, then the answer should be D

3rd year: 40%
2nd year: x
1st year: y

y + 40 = 70 implies y = 30
If y = 30, x = 30 as 40 + x + y = 100

So, y / (x+y) = 30 / 60 = 1/2

[Cybermusings]

1/2 agreed!

[Scott@TargetTestPrep]

In a sample of college students, 40% are third-year students and 70% 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