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Of all the students in a certain dormitory

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Of all the students in a certain dormitory

by m-sand » Sun Dec 27, 2009 9:41 am
Of all the students in a certain dormitory, 1/2 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

OA : B
Last edited by m-sand on Sun Dec 27, 2009 1:57 pm, edited 1 time in total.
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by truplayer256 » Sun Dec 27, 2009 10:41 am
First of all, when you type a question, please make sure you type it correctly. You were missing some important information in this problem. Here's the correct problem:

Of all the students in a certain dormitory, half 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?

Let's assume that there are x students in a certain dormitory.

x/2 are first year students.

x-x/2= x/2 are second year students.

4/5*(x/2)=2x/5 have not declared a major

1/5*x/2=x/10 have declared a major

3*x/10=3x/10 are the amount of second year students who have declared a major.

x/2-3x/10=x/5 are the amount of second year students who have not declared a major.

B is your answer.
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by m-sand » Sun Dec 27, 2009 2:00 pm
truplayer256 wrote:First of all, when you type a question, please make sure you type it correctly. You were missing some important information in this problem. Here's the correct problem:

Of all the students in a certain dormitory, half 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?

Let's assume that there are x students in a certain dormitory.

x/2 are first year students.

x-x/2= x/2 are second year students.

4/5*(x/2)=2x/5 have not declared a major

1/5*x/2=x/10 have declared a major

3*x/10=3x/10 are the amount of second year students who have declared a major.

x/2-3x/10=x/5 are the amount of second year students who have not declared a major.

B is your answer.
Thanks for the explanation.
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