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# Of all the students in a certain dormitory, 1/2 are first-ye

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Of all the students in a certain dormitory, 1/2 are first-ye [#permalink]

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27 Dec 2009, 10:47
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25% (medium)

Question Stats:

77% (02:34) correct 23% (01:52) wrong based on 215 sessions

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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Jan 2013, 07:28, edited 2 times in total.
Renamed the topic and edited the question.
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Re: FDP problem [#permalink]

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27 Dec 2009, 14:31
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I think you dropped a fraction when you typed/copied this in. Working backward from the spoiler answer, I'm thinking the second sentence should read as follows? Please confirm.

"If 4/5 of the first-year students have not declared a major ..."
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Re: FDP problem [#permalink]

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27 Dec 2009, 18:09
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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

OA :
[Reveal] Spoiler:
B

First-year=Second-year=x --> all students $$2x$$;

$$\frac{4}{5}x$$ of the first-year students have not declared a major --> $$\frac{1}{5}x$$ declared;

Second-year students who have declared a major is 3 times the fraction of first-year students who have declared a major =$$\frac{3}{5}x$$ --> who have not $$\frac{2}{5}x$$;

Hence: $$\frac{\frac{2}{5}x}{2x}=\frac{1}{5}$$

Answer: B.
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Re: FDP problem [#permalink]

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27 Dec 2009, 22:10
tot students=x

1st year student=x/2----> non majaor=4/5(x/2)-----> maj=1/5(x/2)

2nd year student=x/2---->maj=3(1/5(x/2))=3/10(x)--->non major=x/2-3/10(x)=1/5(x)

hence 1/5
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Re: FDP problem [#permalink]

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28 Dec 2009, 00:05
1/5...dude form the table as given i manhattan series for sets..this would be a cake walk
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Re: FDP problem [#permalink]

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30 Jan 2013, 07:25
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You can also do this problem sans algebra (in your head):

100 Students Total:

1st yr = 50 students
4/5x50 = 40 = No Major
Therefore: 10 = Major

2nd yr = 50 students
10x3 = 30 = Major
Therefore: 20 = No Major
20/100 = 1/5 = B
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Re: Of all the students in a certain dormitory, 1/2 are first-ye [#permalink]

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08 Jun 2013, 07:34
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In this kind of problem table structure is the weapon for me...

Let 2X would be total student which revealed that 1 yrs student is X and 2nd Yr is X as well.

No form the table

MAJOR NO MAJOR Total Student
1st yr Student x/5 4x/5 x
2nd yr Student 3x/5 2x/5 x
Total Student 4x/5 6x/5 2x

From the table 2nd yr student with major is 2x/5 so the answer would be =2x/5/2x =>1/5 Ans

Rgds
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Re: Of all the students in a certain dormitory, 1/2 are first-ye [#permalink]

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01 Sep 2014, 19:09
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Of all the students in a certain dormitory, 1/2 are first-ye [#permalink]

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03 Sep 2014, 02:26
First ............................................. Second ........................................ Total

x ........................................................ x ................................................ 2x

Major........... NotMajor ................... Major ............ NotMajor ..........

$$\frac{4x}{5}$$ ................ $$\frac{x}{5}$$ ........................ $$\frac{3x}{5}$$ ................... $$\frac{2x}{5}$$ ...................... 2x

Fraction $$= \frac{\frac{2x}{5}}{2x} = \frac{1}{5}$$

Answer = B
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Re: Of all the students in a certain dormitory, 1/2 are first-ye [#permalink]

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28 Apr 2016, 23:06
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Of all the students in a certain dormitory, 1/2 are first-ye   [#permalink] 28 Apr 2016, 23:06
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# Of all the students in a certain dormitory, 1/2 are first-ye

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