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

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In a sample of college students, 40% are third-year students [#permalink]  31 Jan 2004, 10:28
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?

3/4
2/3
4/7
1/2
3/7

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[#permalink]  31 Jan 2004, 10:33
This question looks extremely familiar, yet I don't recall seeing it in any prep material or on any internet boards...

Hmm...
Intern
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[#permalink]  31 Jan 2004, 10:35
Official paper test. Test code 55. Section 3, question 11
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[#permalink]  31 Jan 2004, 10:53
Let us assume that the total number of students are 100
Also, since no info about 4th year is given, we assume that there is no 4th year,

Third Year iii = 40
i + iii (not second year) = 70

Therefore i = 30
ii = 100 - 30 - 40
ii = 30

Ans = ii(2nd year)/ (i + ii) (not third year)
= 30/60
= 1/2
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[#permalink]  01 Feb 2004, 11:16
Got 1/2

Total = S + T + Neither -Both(T & S)

Both(T&S) is zero because student cannot be in two classes.

Let us assume 100 students are there. If 70% are not second year students then 30 students are either thrid year or Neither
Since 40 students are third year then Neither = 30 because
T+Neither = 70 and T = 40
therefore S = 100-70 = 30

Total sudents who are not third year = 100-40 = 60
Students who are in second year = 30
so 30/60 = 1/2
[#permalink] 01 Feb 2004, 11:16
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# In a sample of college students, 40% are third-year students

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