Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 27 May 2016, 00:41

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In a company with 48 employees, some part-time and some full

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 18 Mar 2012
Posts: 48
GMAT 1: 690 Q V
GPA: 3.7
Followers: 0

Kudos [?]: 138 [1] , given: 117

In a company with 48 employees, some part-time and some full [#permalink]

### Show Tags

12 May 2012, 06:26
1
This post received
KUDOS
4
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

59% (02:25) correct 41% (01:30) wrong based on 462 sessions

### HideShow timer Statistics

In a company with 48 employees, some part-time and some full-time, exactly (1/3) of the part-time employees and (1/4) of the full-time 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
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 33037
Followers: 5762

Kudos [?]: 70597 [0], given: 9854

Re: In a company with 48 employees, some part-time and some full [#permalink]

### Show Tags

12 May 2012, 11:51
Expert's post
9
This post was
BOOKMARKED
alexpavlos wrote:
In a company with 48 employees, some part-time and some full-time, exactly (1/3) of the part-time employees and (1/4) of the full-time 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 part-time employees is $$p$$, then # of full-time employees will be $$48-p$$.

We want to maximize $$\frac{p}{3}+\frac{48-p}{4}$$ --> $$\frac{p}{3}+\frac{48-p}{4}=\frac{p+3*48}{12}=\frac{p}{12}+12$$, 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 full-time employees among 48) --> $$\frac{p}{12}+12=3+12=15$$.

Answer: D.

Or: since larger share of part-time employees take the subway then we should maximize # of part-time employees, but we should ensure that $$\frac{p}{3}$$ and $$\frac{48-p}{4}$$ are integers. So $$p$$ should be max multiple of 3 for which $$48-p$$ is a multiple of 4, which turns out to be for $$p=36$$ --> $$\frac{p}{3}+\frac{48-p}{4}=15$$.

Similar question to practice:
in-a-certain-class-consisting-of-36-students-some-boys-and-108870.html
in-a-200-member-association-consisting-of-men-and-women-106175.html
one-week-a-certain-truck-rental-lot-had-a-total-of-15505.html

Hope it helps.
_________________
Manager
Joined: 05 Jun 2010
Posts: 123
Location: India
Concentration: Entrepreneurship, Operations
GMAT 1: 680 Q50 V31
GMAT 2: 690 Q47 V38
GMAT 3: 710 Q49 V39
WE: Design (Manufacturing)
Followers: 1

Kudos [?]: 12 [0], given: 12

Re: In a company with 48 employees, some part-time 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: 142
Location: United States
Concentration: Finance, International Business
GMAT 1: 590 Q28 V38
GPA: 2.54
WE: Accounting (Hospitality and Tourism)
Followers: 1

Kudos [?]: 79 [0], given: 16

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 part-time and some full-time, exactly 1/3 of the engineers are part-time employees and 1/4 of the engineers are full-time 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 time

And you can add step one and two together to get 15.

Tricked me up for a bit
_________________

4/28 GMATPrep 42Q 36V 640

Senior Manager
Joined: 29 Mar 2012
Posts: 287
Concentration: Entrepreneurship
Schools: Kellogg, Kellogg '19
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 25

Kudos [?]: 322 [0], given: 23

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/in-a-company-with-48-employees-some-part-time-and-some-full-132442.html

Regards,
Manager
Joined: 27 Apr 2012
Posts: 62
Location: United States
GMAT Date: 06-11-2013
GPA: 3.5
WE: Marketing (Consumer Products)
Followers: 1

Kudos [?]: 37 [0], given: 21

Re: In a company with 48 employees, some part-time and some full [#permalink]

### Show Tags

13 Jun 2012, 11:39
1
This post was
BOOKMARKED
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 (48-x) = 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: 33037
Followers: 5762

Kudos [?]: 70597 [0], given: 9854

Re: In a company with 48 employees, some part-time and some full [#permalink]

### Show Tags

14 Jun 2013, 05:28
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

All DS Min/Max Problems to practice: search.php?search_id=tag&tag_id=42
All PS Min/Max Problems to practice: search.php?search_id=tag&tag_id=63

_________________
Current Student
Joined: 24 Nov 2012
Posts: 177
Concentration: Sustainability, Entrepreneurship
GMAT 1: 770 Q50 V44
WE: Business Development (Internet and New Media)
Followers: 36

Kudos [?]: 210 [1] , given: 73

Re: In a company with 48 employees, some part-time and some full [#permalink]

### Show Tags

16 Jun 2013, 04:20
1
This post received
KUDOS
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 ... nprep-com/ - 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 - from-the-ashes-thou-shall-rise-770-q-50-v-44-awa-5-ir-162299.html#p1284542

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 9643
Followers: 465

Kudos [?]: 120 [0], given: 0

Re: In a company with 48 employees, some part-time and some full [#permalink]

### Show Tags

18 Aug 2014, 20:15
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Manager
Joined: 22 Feb 2009
Posts: 230
Followers: 5

Kudos [?]: 93 [0], given: 148

Re: In a company with 48 employees, some part-time and some full [#permalink]

### Show Tags

18 Aug 2014, 22:46
1
This post was
BOOKMARKED
alex1233 wrote:
In a company with 48 employees, some part-time and some full-time, exactly (1/3) of the part-time employees and (1/4) of the full-time 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 + (48-P)/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

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 9643
Followers: 465

Kudos [?]: 120 [0], given: 0

Re: In a company with 48 employees, some part-time and some full [#permalink]

### Show Tags

12 Apr 2016, 03:27
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: In a company with 48 employees, some part-time and some full   [#permalink] 12 Apr 2016, 03:27
Similar topics Replies Last post
Similar
Topics:
Martin bought 10 concert tickets, some at the full price of \$2.00 per 4 25 May 2016, 04:56
1 A part-time employee’s hourly wage was increased by 10%. She decided 2 07 Mar 2016, 09:19
1 Of the 150 employees at company X, 80 are full-time, and 100 have work 3 27 Dec 2015, 09:54
Some Qs 9 27 Feb 2010, 20:19
3 There are 135 employees in Company X. If the number of employees who 7 25 Jul 2008, 19:05
Display posts from previous: Sort by

# In a company with 48 employees, some part-time and some full

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.