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Of all the students in a certain dormitory, are first-year

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Manager
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Of all the students in a certain dormitory, are first-year [#permalink] New post 29 Sep 2007, 04:58
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Of all the students in a certain dormitory, ½ are first-year students and the rest are second-year students. 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
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 [#permalink] New post 29 Sep 2007, 06:40
It is B,

1/2 * 1/5 = 1/10 - first year who declared major
3/10 - second year who dec. major
1/2 - 3/10 = 2/10=1/5 portion of total students who is 2-year and did not declared major

Ans: B
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 [#permalink] New post 29 Sep 2007, 07:19
Plug in:

Total students ---> 100

first year ---> 50 ---> declared a major 10 ---> not declared a major 40

second year ---> 50 ---> declared a major 30 ---> not declared a major 20

second-year students who have not declared a major ---> 20/100 = 1/5

:)

Last edited by KillerSquirrel on 29 Sep 2007, 07:29, edited 1 time in total.
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 [#permalink] New post 29 Sep 2007, 07:23
im curious as to where i went wrong:

i started with the info of 4/5th not having selected a major, which gives me:

4/5*(1/2)=2/5 of 1st yrs havent decided a major

This means that 3/5 of 1st yrs have

If the fraction of 2nd yrs who have is 3 times what the first yrs have, this gives me

3*3/5 = 9/5 !!!
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 [#permalink] New post 29 Sep 2007, 07:36
pmenon wrote:
im curious as to where i went wrong:

i started with the info of 4/5th not having selected a major, which gives me:

4/5*(1/2)=2/5 of 1st yrs havent decided a major

This means that 3/5 of 1st yrs have

If the fraction of 2nd yrs who have is 3 times what the first yrs have, this gives me

3*3/5 = 9/5 !!!


this is a non sequitur ! since 1-2/5 = 3/5 will give you P(second year declared a major)+P(second year not declared a major)+P(first year declared a major) and not ---> P(first year declared a major) = 3/5

:)
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Re: PS - fraction [#permalink] New post 01 Oct 2007, 11:26
Balvinder wrote:
Of all the students in a certain dormitory, ½ are first-year students and the rest are second-year students. 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


B.

used a double set matrix.
Column 1 = 1 st yr
Column 2 = 2 nd yr
Row 1 = Decl. Major
Row 2 = Not Decl.

Column 3 and Row 3 = Total.

If total = x; 1st yr = 1/2x; 2nd yr = 1/2x
1st yr not decl = 2/5 x
1 st yr decl = 1/2x - 2/5x = 1/10x
2nd yr decl = 3/10 x
2nd yr not decl = 1/2x - 3/10x = 1/5x
Re: PS - fraction   [#permalink] 01 Oct 2007, 11:26
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