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Of all the students in a certain dormitory, 1/2 are first-year student

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Re: Of all the students in a certain dormitory, 1/2 are first-year student [#permalink] New post   21 Nov 2020, 19:07
Table Method is the way to go

Take the total as 100, something that is divisible by all fractions given in the question, so as to solve this without any complicated fractions/calculations.

You will get 20/100 or 1/5 as the answer.

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Re: Of all the students in a certain dormitory, 1/2 are first-year student [#permalink] New post   24 Nov 2020, 11:19
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msand wrote:
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



Let all student of the dormitory = 120

First-year student = 60

Second year student= 60

Students of first year who declared major \(= (1-\frac{4}{5})=\frac{1}{5}\) \(=60*\frac{1}{5 }= 12\)

Students of the second year who declared major \(= 12*3=36\)

Student of the second year, who didn't declare major \(= 60-36=24\)

\(\frac{second-year \ students \ who \ have \ not \ declared \ a \ major}{Total \ students of \ the \ dormitory} = \frac{24}{120}=\frac{2}{10}=\frac{1}{5}\)

The answer is \(B\)
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Re: Of all the students in a certain dormitory, 1/2 are first-year student [#permalink] New post   24 Jan 2021, 17:22
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msand wrote:
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


Total Students \(= 60 \)

First year's \(= 30;\) Do not declared major \(=30*\frac{4}{5}=24\), Declared maror \(=6\)

Second year's 30, Declared major 6*3=18, don't declared major \(30-18=12\)

The fraction \(\frac{12}{60}=\frac{1}{5}\)

The answer is B
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Re: Of all the students in a certain dormitory, 1/2 are first-year student [#permalink] New post   02 Feb 2021, 22:12
I was confused between 1/5 and 2/5 ,how to know whether they want the total from the whole set of students or just the second year ones?
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Re: Of all the students in a certain dormitory, 1/2 are first-year student [#permalink] New post   18 Apr 2021, 01:26
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msand wrote:
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


Answer: Option B

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Of all the students in a certain dormitory, 1/2 are first-year student [#permalink] New post   08 Oct 2021, 09:24
ImChasmish

It was mentioned in the last line "what fraction of all the students in the dormitory are second-year students who have not declared a major?
What fraction from all the students = Total students (denominator), so fraction is out of all the students (first + second year)
second-year students who have not declared a major - Numerator

ImChasmish wrote:
I was confused between 1/5 and 2/5 ,how to know whether they want the total from the whole set of students or just the second year ones?
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Re: Of all the students in a certain dormitory, 1/2 are first-year student [#permalink] New post   07 Nov 2023, 04:00
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Re: Of all the students in a certain dormitory, 1/2 are first-year student [#permalink]
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