GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Nov 2019, 18:29

### 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

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

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 18 Mar 2012
Posts: 45
GPA: 3.7
In a company with 48 employees, some part-time and some full  [#permalink]

### Show Tags

12 May 2012, 06:26
3
22
00:00

Difficulty:

55% (hard)

Question Stats:

63% (01:55) correct 37% (02:09) wrong based on 585 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
Math Expert
Joined: 02 Sep 2009
Posts: 59075
Re: In a company with 48 employees, some part-time and some full  [#permalink]

### Show Tags

12 May 2012, 11:51
4
14
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) --> $$\frac{p}{12}+12=3+12=15$$.

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

Hope it helps.
_________________
##### General Discussion
Manager
Joined: 05 Jun 2010
Posts: 120
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 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: 113
Location: United States
GMAT 1: 590 Q28 V38
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 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
Current Student
Joined: 29 Mar 2012
Posts: 295
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/in-a-company-with-48-employees-some-part-time-and-some-full-132442.html

Regards,
Manager
Joined: 27 Apr 2012
Posts: 57
Location: United States
GMAT Date: 06-11-2013
GPA: 3.5
WE: Marketing (Consumer Products)
Re: In a company with 48 employees, some part-time and some full  [#permalink]

### Show Tags

13 Jun 2012, 11:39
1
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: 59075
Re: In a company with 48 employees, some part-time and some full  [#permalink]

### Show Tags

14 Jun 2013, 05:28
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

_________________
Manager
Joined: 24 Nov 2012
Posts: 143
Concentration: Sustainability, Entrepreneurship
GMAT 1: 770 Q50 V44
WE: Business Development (Internet and New Media)
Re: In a company with 48 employees, some part-time and some full  [#permalink]

### Show Tags

16 Jun 2013, 04:20
1
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/cbermanmanhattanprep-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 - http://gmatclub.com/forum/from-the-ashes-thou-shall-rise-770-q-50-v-44-awa-5-ir-162299.html#p1284542
Manager
Joined: 22 Feb 2009
Posts: 154
Re: In a company with 48 employees, some part-time and some full  [#permalink]

### Show Tags

18 Aug 2014, 22:46
1
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
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15454
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In a company with 48 employees, some part-time and some full  [#permalink]

### Show Tags

13 Jan 2018, 17:27
1
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 part-time and some full-time.

Since 1/3 of the part-timers take the subway to work, we know that the number of part-timers MUST be a MULTIPLE OF 3.
Since 1/4 of the full-timers take the subway to work, we know that the number of full-timers 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 part-timers (since a greater fraction of that group (than the fraction of full-timers) 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 full-timers + 1/3 of 36 part-timers =

3 + 12 = 15

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Manager
Joined: 30 Apr 2017
Posts: 98
Location: India
GMAT 1: 700 Q47 V39
GPA: 3.4
Re: In a company with 48 employees, some part-time 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
Senior Manager
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 440
Re: In a company with 48 employees, some part-time and some full  [#permalink]

### Show Tags

25 Mar 2019, 14:45
I made the mistake of doing it this way:

1) Set up equation 3x+4y = 48
2) 48/7 = 6 R6, which means with 6 of each (or 18 + 24) and there's 6 remaining, which is also divisible by 3... so 24 + 24.
3) 8+6 = 14 people, this is the trap answer C.

As Rich pointed out, we actually get +1 more person by splitting them 36 + 12 (12 + 3 people)
Re: In a company with 48 employees, some part-time and some full   [#permalink] 25 Mar 2019, 14:45
Display posts from previous: Sort by