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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

6

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

59% (02:26) correct
41% (01:30) wrong based on 485 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?

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 \(p=36\) --> \(\frac{p}{3}+\frac{48-p}{4}=15\).

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.

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

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.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

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. _________________

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?

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. _________________

This is the kickoff for my 2016-2017 application season. After a summer of introspect and debate I have decided to relaunch my b-school application journey. Why would anyone want...

Check out this awesome article about Anderson on Poets Quants, http://poetsandquants.com/2015/01/02/uclas-anderson-school-morphs-into-a-friendly-tech-hub/ . Anderson is a great place! Sorry for the lack of updates recently. I...

According to the Nebula Award categories, a novel must be over 40,000 words. In the past year I have written assignments for 22 classes totaling just under 65...