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

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New post 12 Aug 2011, 15:23
I think the answer choices you have provided because the answer cannot be greater than one.

Here is an easy way to think about this is by picking "smart" numbers.
Let's pick 50 for the first half of students who are 1st years and 50 for the other half who are 2nd year.
We know that 4/5 of the 1st years have not declared a major so that gives us 50*4/5=40, so 10 have declared a major.
We also know that the number of 2nd year that have not declared a major = 3 times the # of 1st year who have declared a major. This gives us 3*10=30

The question asks for fraction of 2nd years who have not declared a major over the total students.
30 have declared a major out of the 2nd year so 20 have not. Since we have 100 students (50+50), the answer is 20/100 or 1/5.

You can run a search on the web and you will find this question without the correct answer choices.

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Re: FDP problem [#permalink]

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New post 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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New post 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

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

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

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

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

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

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Attached is a visual that should help.

FY = First Year
SY = Second Year
NDM = Not Decided on Major
YDM = Yes Decided on Major
SYY = Senior Year Yes
SYN = Senior Year No


Attachments

Screen Shot 2016-05-05 at 6.59.42 PM.png
Screen Shot 2016-05-05 at 6.59.42 PM.png [ 68.47 KiB | Viewed 768 times ]


Last edited by mcelroytutoring on 07 May 2016, 21:08, edited 6 times in total.
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Re: Of all the students in a certain dormitory, 1/2 are first-year student [#permalink]

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New post 05 May 2016, 21:38
mojorising800 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. 151
B. 51
C. 154
D. 31
E. 52


Say there are in all 100 students. Use a matrix:
50 are first year and 50 are second year students.

........................Major Dec................Major not dec..............Total
First Year............................................................................50
Second Yr...........................................................................50
Total

4/5 * 50 = 40 not declared major first year students.

........................Major Dec................Major not dec..............Total
First Year................10..................................40....................50
Second Yr...........................................................................50
Total

second-year students who have declared a major is 3 times the fraction of first-year students who have declared a major

........................Major Dec................Major not dec..............Total
First Year................10..................................40.....................50
Second Yr...............30..................................20......................50
Total

So second year students who've not declared a major is 20/100 = 1/5

Answer (B)
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Re: Of all the students in a certain dormitory, 1/2 are first-year student [#permalink]

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New post 27 Jun 2016, 05:51
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The answer choices provided are not correct!

I solved the question using LCM method. The solution is given below:

Assume the total number of stuents to be 30, LCM(2,3,5)

Now, as per the given info, half the students are 1st year. Therefore, there are 15 students each in 1st and 2nd year.
We can further calculate the students who have selected majors in 1st year and second year. And, finally we can calculate the fraction for answering the question

Correct answer - 1/5
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Re: Of all the students in a certain dormitory, 1/2 are first-ye [#permalink]

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New post 27 Jun 2016, 06:22
samratpahwa wrote:
The answer choices provided are not correct!

I solved the question using LCM method. The solution is given below:

Assume the total number of stuents to be 30, LCM(2,3,5)

Now, as per the given info, half the students are 1st year. Therefore, there are 15 students each in 1st and 2nd year.
We can further calculate the students who have selected majors in 1st year and second year. And, finally we can calculate the fraction for answering the question

Correct answer - 1/5


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

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New post 27 Jun 2016, 08:04
\((1-(1-4/5)*3)*(1-1/2)=1/5\)

Answer choice B.
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Re: Of all the students in a certain dormitory, 1/2 are first-ye   [#permalink] 27 Jun 2016, 08:04
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