Jul 20 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Jul 21 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes Jul 26 08:00 AM PDT  09:00 AM PDT The Competition Continues  Game of Timers is a teambased competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Ends July 26th Jul 27 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 27 Dec 2009
Posts: 134

Of all the students in a certain dormitory, 1/2 are firstyear student
[#permalink]
Show Tags
Updated on: 22 Aug 2017, 11:43
Question Stats:
78% (02:12) correct 22% (02:27) wrong based on 1126 sessions
HideShow timer Statistics
Of all the students in a certain dormitory, 1/2 are firstyear students and the rest are secondyear students. If 4/5 of the firstyear students have not declared a major and if the fraction of secondyear students who have declared a major is 3 times the fraction of firstyear students who have declared a major, what fraction of all the students in the dormitory are secondyear students who have not declared a major? A. 1/15 B. 1/5 C. 4/15 D. 1/3 E. 2/5
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by msand on 27 Dec 2009, 10:47.
Last edited by Bunuel on 22 Aug 2017, 11:43, edited 3 times in total.
Renamed the topic and edited the question.



Math Expert
Joined: 02 Sep 2009
Posts: 56300

Re: Of all the students in a certain dormitory, 1/2 are firstyear student
[#permalink]
Show Tags
27 Dec 2009, 18:09
msand wrote: Of all the students in a certain dormitory, 1/2 are firstyear students and the rest are secondyear students. If 4/5 of the firstyear students have not declared a major and if the fraction of secondyear students who have declared a major is 3 times the fraction of firstyear students who have declared a major, what fraction of all the students in the dormitory are secondyear students who have not declared a major? A. 1/15 B. 1/5 C. 4/15 D. 1/3 E. 2/5 OA : Firstyear=Secondyear=x > all students \(2x\); \(\frac{4}{5}x\) of the firstyear students have not declared a major > \(\frac{1}{5}x\) declared; Secondyear students who have declared a major is 3 times the fraction of firstyear 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.
_________________



Manager
Joined: 09 May 2009
Posts: 173

Re: Of all the students in a certain dormitory, 1/2 are firstyear student
[#permalink]
Show Tags
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/23/10(x)=1/5(x) hence 1/5
_________________
GMAT is not a game for losers , and the moment u decide to appear for it u are no more a loser........ITS A BRAIN GAME



Intern
Joined: 14 May 2010
Posts: 7
Location: US
Schools: Said, Judge, HEC, Cornell, Darden, Columbia, Notre Dame, NYU, Kellog, INSEAD, Emory
WE 1: Consulting at Big 4

Re: Of all the students in a certain dormitory, 1/2 are firstyear student
[#permalink]
Show Tags
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.
Thanks



Intern
Affiliations: SAGAFTRA, AEA
Joined: 27 May 2011
Posts: 11
Location: United States
Concentration: Technology, Strategy
GMAT Date: 04202013
WE: Performing Arts (Entertainment and Sports)

Re: Of all the students in a certain dormitory, 1/2 are firstyear student
[#permalink]
Show Tags
30 Jan 2013, 07:25
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 students10x3 = 30 = Major Therefore: 20 = No Major 20/100 = 1/5 = B
_________________
"How far that little candle throws his beams. So shines a good deed in a weary world."  Shakespeare



Manager
Joined: 26 Feb 2012
Posts: 97
Location: India
Concentration: General Management, Finance
WE: Engineering (Telecommunications)

Re: Of all the students in a certain dormitory, 1/2 are firstyear student
[#permalink]
Show Tags
08 Jun 2013, 07:34
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 Prasannajeet



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1787
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: Of all the students in a certain dormitory, 1/2 are firstyear student
[#permalink]
Show Tags
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
_________________
Kindly press "+1 Kudos" to appreciate



Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 696
Location: United States (CA)
Age: 39
GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42
WE: Education (Education)

Re: Of all the students in a certain dormitory, 1/2 are firstyear student
[#permalink]
Show Tags
Updated on: 07 May 2016, 21:08
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 20160505 at 6.59.42 PM.png [ 68.47 KiB  Viewed 8096 times ]
_________________
Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching worldwide since 2002. One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V. You can download my official testtaker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y7knw7bt Date of Birth: 09 December 1979. GMAT Action Plan and Free EBook  McElroy TutoringContact: mcelroy@post.harvard.edu (I do not respond to PMs on GMAT Club.) ...or find me on Reddit: http://www.reddit.com/r/GMATpreparation



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9443
Location: Pune, India

Re: Of all the students in a certain dormitory, 1/2 are firstyear student
[#permalink]
Show Tags
05 May 2016, 21:38
mojorising800 wrote: Of all the students in a certain dormitory, 1/2 are firstyear students and the rest are secondyear students. If 4/5 of the firstyear students have not declared a major and if the fraction of secondyear students who have declared a major is 3 times the fraction of firstyear students who have declared a major, what fraction of all the students in the dormitory are secondyear 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 secondyear students who have declared a major is 3 times the fraction of firstyear 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)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Senior Manager
Joined: 24 Jun 2016
Posts: 340
GPA: 4

Re: Of all the students in a certain dormitory, 1/2 are firstyear student
[#permalink]
Show Tags
27 Jun 2016, 08:04
\((1(14/5)*3)*(11/2)=1/5\) Answer choice B.
_________________
Stuck in the 600's and want to score 700+ on the GMAT? If this describes you, we should talk. I specialize in getting motivated students into the 700's.$75/hour as of July 2019. I am not accepting any more students for the Fall 2019 application cycle, but if you are planning to apply in 2020, feel free to reach out! http://www.facebook.com/HanoiGMATtutorHanoiGMATTutor@gmail.com



Manager
Joined: 21 Jun 2017
Posts: 83

Of all the students in a certain dormitory, 1/2 are firstyear student
[#permalink]
Show Tags
Updated on: 07 Oct 2017, 07:33
This problem is 99 in og 2017. T = total students in dorm 4/5 first year no declared major = 4/5(.5T) = .4T = # first year no major .5T  .4T = .1T = 1st year w/ major .1T x 3 = .3T 2nd year no major = .5T  .3T = .2T = 2nd no declared . 2T does not equal 2/5!.2T / T = .2 = 1/5
Originally posted by CyberStein on 22 Aug 2017, 11:32.
Last edited by CyberStein on 07 Oct 2017, 07:33, edited 1 time in total.



Senior SC Moderator
Joined: 22 May 2016
Posts: 3087

Re: Of all the students in a certain dormitory, 1/2 are firstyear student
[#permalink]
Show Tags
22 Aug 2017, 16:05
msand wrote: Of all the students in a certain dormitory, 1/2 are firstyear students and the rest are secondyear students. If 4/5 of the firstyear students have not declared a major and if the fraction of secondyear students who have declared a major is 3 times the fraction of firstyear students who have declared a major, what fraction of all the students in the dormitory are secondyear students who have not declared a major?
A. 1/15 B. 1/5 C. 4/15 D. 1/3 E. 2/5 Attachment:
matrix111.png [ 17.63 KiB  Viewed 6299 times ]
Double matrix works well here, at least for me. I assumed 60 total students. 1. Number of dormitory students = 60. Half are firstyear students = 30. So the other half, secondyear students = 302. \(\frac{4}{5}\) of firstyear students have NOT declared a major: \(\frac{4}{5}\) * 30 = 243. Firstyear students who HAVE declared a major = 30 total  24 not = 6 who have 4. The fraction of secondyear students who have declared a major is three times the fraction of firstyear students who have declared a major. Firstyear declared = 6. Secondyear declared = 3 * 6 = 185. Secondyear students who have NOT declared a major: 30 total secondyear students  18 who have declared = 12 secondyear students who have not 6. What fraction of ALL students are secondyear students who have not declared a major? \(\frac{12}{60} = \frac{1}{5}\)Answer B
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here. Take another look. Take a look around. These are the moments you can't pass by.



Manager
Status: Searching for something I've been searching..LOL
Joined: 14 Dec 2016
Posts: 57
Location: India
Concentration: Healthcare, Operations
GPA: 3.5
WE: Medicine and Health (Health Care)

Of all the students in a certain dormitory, 1/2 are firstyear student
[#permalink]
Show Tags
23 Aug 2017, 00:45
msand wrote: Of all the students in a certain dormitory, 1/2 are firstyear students and the rest are secondyear students. If 4/5 of the firstyear students have not declared a major and if the fraction of secondyear students who have declared a major is 3 times the fraction of firstyear students who have declared a major, what fraction of all the students in the dormitory are secondyear students who have not declared a major?
A. 1/15 B. 1/5 C. 4/15 D. 1/3 E. 2/5 This question is pretty easy if we assume numbers. Used numbers because the question does not have fixed values and asks for percentages. Assuming the total number of students in the dormitory to be 100 Given 1/2 are 1st year and other 1/2 are 2nd year. Hence 50 students each are in either year. Given 1st year (Not decided Major)= 1stNDM=4/5th of 1st year=40 Hence 1st year (Decided Major)= 1stDM=10 Given 2nd year (Decided Major)= 2ndDM=3x1stDM=30 Hence 2nd year (Not decided Major)= 2ndNDM=100(40+10+30)=20 Fraction of 2nd year students who havent declared a major = 20/100=1/5



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6968
Location: United States (CA)

Re: Of all the students in a certain dormitory, 1/2 are firstyear student
[#permalink]
Show Tags
07 Jun 2018, 17:10
msand wrote: Of all the students in a certain dormitory, 1/2 are firstyear students and the rest are secondyear students. If 4/5 of the firstyear students have not declared a major and if the fraction of secondyear students who have declared a major is 3 times the fraction of firstyear students who have declared a major, what fraction of all the students in the dormitory are secondyear students who have not declared a major?
A. 1/15 B. 1/5 C. 4/15 D. 1/3 E. 2/5 Since 1/2 are firstyear students, the other 1/2 are secondyear students. Since 4/5 of the firstyear students have not declared a major, so 1/5 of them have declared a major. Since the fraction of secondyear students who have declared a major is 3 times the fraction of firstyear students who have declared a major, 3/5 of the secondyear students have declared a major. Therefore, 2/5 of the secondyear students have not declared a major. Since the secondyear students are 1/2 of all the students, 1/2 x 2/5 = 1/5 of all students are secondyear students who have not declared a major. Answer: B
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



IIMA, IIMC School Moderator
Joined: 04 Sep 2016
Posts: 1361
Location: India
WE: Engineering (Other)

Re: Of all the students in a certain dormitory, 1/2 are firstyear student
[#permalink]
Show Tags
05 Jul 2018, 19:47
pushpitkc niks18 Abhishek009 pikolo2510 Is there any better approach to find LCM of ordered set {2,3,5}? I normally find the smallest multiple of largest no (here: 5) and see if it is divisible by other two elements in set. Also VeritasPrepKarishma made calculations bit easier by using starting number as 100 instead of taking LCM in spite of no percentage mentioned in problem. How do we get a hint about it?
_________________
It's the journey that brings us happiness not the destination. Feeling stressed, you are not alone!!



Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3359
Location: India
GPA: 3.12

Re: Of all the students in a certain dormitory, 1/2 are firstyear student
[#permalink]
Show Tags
06 Jul 2018, 00:14
adkikani wrote: pushpitkc niks18 Abhishek009 pikolo2510 Is there any better approach to find LCM of ordered set {2,3,5}? I normally find the smallest multiple of largest no (here: 5) and see if it is divisible by other two elements in set. Also VeritasPrepKarishma made calculations bit easier by using starting number as 100 instead of taking LCM in spite of no percentage mentioned in problem. How do we get a hint about it? Hi adkikaniWhat do you mean by a better approach to finding the LCM of the ordered set? IMO, using the LCM of the numbers is always a better choice instead of going with a random number. When you use a random number, there is a chance of reaching a stage where you might reach a fraction and have to restart the process. For this problem, you can see the method used by generis to assume 30(LCM of 2,3,5). The more questions you practice using this method, you will get better at choosing numbers. Hope that helps you
_________________
You've got what it takes, but it will take everything you've got



Manager
Joined: 17 May 2015
Posts: 248

Re: Of all the students in a certain dormitory, 1/2 are firstyear student
[#permalink]
Show Tags
06 Jul 2018, 00:36
adkikani wrote: Is there any better approach to find LCM of ordered set {2,3,5}?
I normally find the smallest multiple of largest no (here: 5) and see if it is divisible by other two elements in set. Hi adkikani, Rather taking multiple of 5 and checking every time, you can simply multiply 2*3*5 = 30. Now, suppose we have another 3 numbers say 12, 30, and 35. To find LCM you can also use the prime factorization method. \(12 = 2^2 *3\) 30 = 5*3*2 35 = 5*7 Now, take the maximum power of each prime number and multiply. LCM = 2^2*3*5*7 = 420. Hope this helps. Thanks.



Intern
Joined: 28 Apr 2016
Posts: 42
Location: United States
GPA: 3.9

Of all the students in a certain dormitory, 1/2 are firstyear student
[#permalink]
Show Tags
11 Aug 2018, 18:48
If you are looking for more questions to practice the matrix box (also called double matrix) approach, I have compiled a list of questions from the Official Guide and Veritas Prep books at this link: Matrix BoxesFor time efficiency, I generally recommend using a matrix box whenever you see a question that divides up a group into two categories in two different ways. I recommend drawing a matrix box that looks essentially like the one that generis posted in this thread. To me, matrix boxes improve efficiency because they help you to see the information in an organized way. You can also mark the boxes that you need to fill in to answer the question, so that you know exactly when you can stop because you have the information you need. Please let me know if you have any questions, and if you want me to post a video solution!
_________________
Online GMAT tutor with a 780 GMAT score. Harvard graduate. Please read and share my free GMAT Timing Strategy Guide!



Senior Manager
Joined: 04 Aug 2010
Posts: 435
Schools: Dartmouth College

Re: Of all the students in a certain dormitory, 1/2 are firstyear student
[#permalink]
Show Tags
11 Aug 2018, 19:09
msand wrote: Of all the students in a certain dormitory, 1/2 are firstyear students and the rest are secondyear students. If and if the fraction of secondyear students who have declared a major is 3 times the fraction of firstyear students who have declared a major, what fraction of all the students in the dormitory are secondyear students who have not declared a major?
A. 1/15 B. 1/5 C. 4/15 D. 1/3 E. 2/5 I would use a doublematrix to organize the data. That said, here is an alternate approach: Since \(\frac{4}{5}\) of the firstyear students have not declared a major, \(\frac{1}{5}\) of the firstyear students HAVE declared a major. Since the fraction of secondyear students who have declared a major is 3 times the fraction of firstyear students who have declared a major, \(\frac{3}{5}\) of the secondyear students have declared a major, implying that \(\frac{2}{5}\) of the secondyear students have NOT declared a major. Since \(\frac{1}{2}\) of the students are secondyear students, and \(\frac{2}{5}\) of these secondyear students have not declared a major, \(\frac{1}{2} * \frac{2}{5} = \frac{1}{5}\) of the students are secondyear students who have not declared a major.
_________________
GMAT and GRE Tutor Over 1800 followers GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and longdistance. For more information, please email me at GMATGuruNY@gmail.com.



Intern
Joined: 19 May 2016
Posts: 23
Location: Pakistan
Concentration: Marketing, Strategy
GPA: 3.1

Re: Of all the students in a certain dormitory, 1/2 are firstyear student
[#permalink]
Show Tags
18 Dec 2018, 20:43
MATRIX BOX is the way to solve a question like this!




Re: Of all the students in a certain dormitory, 1/2 are firstyear student
[#permalink]
18 Dec 2018, 20:43






