Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 18 Mar 2012
Posts: 47
GPA: 3.7

In a company with 48 employees, some parttime and some full [#permalink]
Show Tags
12 May 2012, 06:26
Question Stats:
63% (01:28) correct 37% (01:38) wrong based on 621 sessions
HideShow timer Statistics
In a company with 48 employees, some parttime and some fulltime, exactly (1/3) of the parttime employees and (1/4) of the fulltime employees take the subway to work. What is the greatest possible number of employees who take the subway to work? A. 12 B. 13 C. 14 D. 15 E. 16
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 46305

Re: In a company with 48 employees, some parttime and some full [#permalink]
Show Tags
12 May 2012, 11:51
alexpavlos wrote: In a company with 48 employees, some parttime and some fulltime, exactly (1/3) of the parttime employees and (1/4) of the fulltime employees take the subway to work. What is the greatest possible number of employees who take the subway to work?
A. 12 B. 13 C. 14 D. 15 E. 16
Found this question; I can do it by picking numbers, however whats the algebraic solution to it? Say # of parttime employees is \(p\), then # of fulltime employees will be \(48p\). We want to maximize \(\frac{p}{3}+\frac{48p}{4}\) > \(\frac{p}{3}+\frac{48p}{4}=\frac{p+3*48}{12}=\frac{p}{12}+12\), so we should maximize \(p\), but also we should make sure that \(\frac{p}{12}+12\) remains an integer (as it represent # of people). Max value of \(p\) for which p/12 is an integer is for \(p=36\) (p can not be 48 as we are told that there are some # of fulltime employees among 48) > \(\frac{p}{12}+12=3+12=15\). Answer: D. Or: since larger share of parttime employees take the subway then we should maximize # of parttime employees, but we should ensure that \(\frac{p}{3}\) and \(\frac{48p}{4}\) are integers. So \(p\) should be max multiple of 3 for which \(48p\) is a multiple of 4, which turns out to be for \(p=36\) > \(\frac{p}{3}+\frac{48p}{4}=15\). Similar question to practice: inacertainclassconsistingof36studentssomeboysand108870.htmlina200memberassociationconsistingofmenandwomen106175.htmloneweekacertaintruckrentallothadatotalof15505.htmlHope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 05 Jun 2010
Posts: 121
Location: India
Concentration: Entrepreneurship, Operations
GMAT 1: 680 Q50 V31 GMAT 2: 690 Q47 V38 GMAT 3: 710 Q49 V39
WE: Design (Manufacturing)

Re: In a company with 48 employees, some parttime and some full [#permalink]
Show Tags
12 May 2012, 14:00
Let part time emp=x Let full time emp=y then, 48=x+y.........(1) (1/3)x+(1/4)y=No. of ppl taking the subway 4x+3y/12=No. of ppl taking the subway using 1 x/12+3*48/12=No. of ppl taking the subway so, the minimum value of x has to be 12. Hence to maximize the no. put 36 for x 36/12+12/4=15 Hope that helps!!
_________________
Work with hope in Heart and dreams in the eyes .... And leave the mind for GMAT problems



Manager
Joined: 29 Mar 2010
Posts: 128
Location: United States
Concentration: Finance, International Business
GPA: 2.54
WE: Accounting (Hospitality and Tourism)

Re: CAN SOMEONE HELP SOLVE THIS PS [#permalink]
Show Tags
12 Jun 2012, 11:21
prakash111687 wrote: Hi can someone let me know how the below problem can be solved efficiently.
A some engineering firm with 48 employees, in that some are parttime and some fulltime, exactly 1/3 of the engineers are parttime employees and 1/4 of the engineers are fulltime employees take the bus as a mean of transportation to work. What is the greatest possible number of engineers who take the bus as a mean of transportation to work?
A) 12 B) 13 C) 14 D) 15 E) 16 Step 1) If you know that 1/4 of the employees are full time and ride the bus you can multiply .25*48 = 12 Step 2) find the difference between 1/3 and 1/4 = 1/12 * 48= 3 # of people that take the bus every day regardless of whether they are full or part timeAnd you can add step one and two together to get 15. Tricked me up for a bit
_________________
4/28 GMATPrep 42Q 36V 640



Current Student
Joined: 29 Mar 2012
Posts: 317
Location: India
GMAT 1: 640 Q50 V26 GMAT 2: 660 Q50 V28 GMAT 3: 730 Q50 V38

Re: CAN SOMEONE HELP SOLVE THIS PS [#permalink]
Show Tags
12 Jun 2012, 23:35
Quote: Step 2) find the difference between 1/3 and 1/4 = 1/12 * 48= [b]3
Hi, Firstly, 1/12*48 = 4 Secondly, You may find the correct question & solution here: http://gmatclub.com/forum/inacompanywith48employeessomeparttimeandsomefull132442.htmlRegards,



Manager
Joined: 27 Apr 2012
Posts: 58
Location: United States
GMAT Date: 06112013
GPA: 3.5
WE: Marketing (Consumer Products)

Re: In a company with 48 employees, some parttime and some full [#permalink]
Show Tags
13 Jun 2012, 11:39
Hi,just wanted to share my method. Let the number of part time employees = x therefore,the number of full time employees = (48  x) 1/3x + 1/4 (48x) = number of people who take the subway Since the number that constitutes "x" needs to be a multiple of both 3 & 4 and needs to be less than 48, we take the LCM of 3,4 i.e. 12 and consider all common multiples until 48. Hence we get 12,24,36 which are common multiples and < 48. The question asks for the max number so plug in : 1/3(12) + 1/4(36) = 4 + 9 = 13 1/3(24) + 1/4(24) = 8 + 6 = 14 1/3(36) + 1/4(12) = 12 + 3 = 15 > maximum number and hence the answer



Math Expert
Joined: 02 Sep 2009
Posts: 46305

Re: In a company with 48 employees, some parttime and some full [#permalink]
Show Tags
14 Jun 2013, 05:28



Manager
Joined: 24 Nov 2012
Posts: 171
Concentration: Sustainability, Entrepreneurship
WE: Business Development (Internet and New Media)

Re: In a company with 48 employees, some parttime and some full [#permalink]
Show Tags
16 Jun 2013, 04:20
An easier approach... We know that the number of part time employees taking the bus must be divisible by 3 and full time by 4 and in order to maximize the number the number of part time employees should be higher. So i just jotted down a table of possible combos from 48 part time 0 full time as below, reducing 3 from 48 as i went down and chose the first option where the number of fulltime employees will be divisible by 4 Part Time Full Time Comment 48 0 Not valid as there is some number of Full time employees as per question 45 3 FT not divisible by 4 42 6 FT not divisible by 4 39 9 FT not divisible by 4 36 12 This is our answer So number = 36/3 + 12/4 = 15
_________________
You've been walking the ocean's edge, holding up your robes to keep them dry. You must dive naked under, and deeper under, a thousand times deeper!  Rumi
http://www.manhattangmat.com/blog/index.php/author/cbermanmanhattanprepcom/  This is worth its weight in gold
Economist GMAT Test  730, Q50, V41 Aug 9th, 2013 Manhattan GMAT Test  670, Q45, V36 Aug 11th, 2013 Manhattan GMAT Test  680, Q47, V36 Aug 17th, 2013 GmatPrep CAT 1  770, Q50, V44 Aug 24th, 2013 Manhattan GMAT Test  690, Q45, V39 Aug 30th, 2013 Manhattan GMAT Test  710, Q48, V39 Sep 13th, 2013 GmatPrep CAT 2  740, Q49, V41 Oct 6th, 2013
GMAT  770, Q50, V44, Oct 7th, 2013 My Debrief  http://gmatclub.com/forum/fromtheashesthoushallrise770q50v44awa5ir162299.html#p1284542



Manager
Joined: 22 Feb 2009
Posts: 194

Re: In a company with 48 employees, some parttime and some full [#permalink]
Show Tags
18 Aug 2014, 22:46
alex1233 wrote: In a company with 48 employees, some parttime and some fulltime, exactly (1/3) of the parttime employees and (1/4) of the fulltime employees take the subway to work. What is the greatest possible number of employees who take the subway to work?
A. 12 B. 13 C. 14 D. 15 E. 16 P/3 + F/4 = P/3 + (48P)/4 = 12 + P/2 P/3 + F/3 = (P+F)/3 = 48/3 = 16 P/4 + F/4 = 12 P/3 + F/3 > P/3 + F/4 > P/4 + F/4 > 16> 12 + P/12 > 12 GREATEST Possible: 12 + p/12 = 15 > p = 36 ( integer > good) 15 or D is the answer
_________________
......................................................................... +1 Kudos please, if you like my post



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11837
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: In a company with 48 employees, some parttime and some full [#permalink]
Show Tags
13 Jan 2018, 17:27
Hi All, This type of question is rare on Test Day (you might see 1) and the shortcuts that are built into it are more about logic than anything else. If you're not sure how to start off this question, then you might have to do a bit of "brute force" (throw some numbers at it and see if a pattern emerges. We know that there are 48 employees, some parttime and some fulltime. Since 1/3 of the parttimers take the subway to work, we know that the number of parttimers MUST be a MULTIPLE OF 3. Since 1/4 of the fulltimers take the subway to work, we know that the number of fulltimers MUST be a MULTIPLE OF 4. So we need a multiple of 4 added to a multiple of 3 that totals 48. We also want to MAXIMIZE the number of workers that take the subway, which means that we want to maximize the number of parttimers (since a greater fraction of that group (than the fraction of fulltimers) takes the subway). To find that perfect set of numbers, I'm going to start with multiples of 4 and see what happens…. 4 > 44 left (not a multiple of 3) 8 > 40 left (not a multiple of 3) 12 > 36 left (this IS a multiple of 3) So 1/4 of 12 fulltimers + 1/3 of 36 parttimers = 3 + 12 = 15 Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Manager
Joined: 30 Apr 2017
Posts: 79

Re: In a company with 48 employees, some parttime and some full [#permalink]
Show Tags
13 Jan 2018, 17:49
Gonnaflynow wrote: Let part time emp=x Let full time emp=y
then,
48=x+y.........(1)
(1/3)x+(1/4)y=No. of ppl taking the subway
4x+3y/12=No. of ppl taking the subway
using 1
x/12+3*48/12=No. of ppl taking the subway
so, the minimum value of x has to be 12.
Hence to maximize the no. put 36 for x
36/12+12/4=15
Hope that helps!! In the last step, it should be 36/12 + 48/4 = 15. Cheers, Kabir




Re: In a company with 48 employees, some parttime and some full
[#permalink]
13 Jan 2018, 17:49






