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

Question

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?

A. 12
B. 13
C. 14
D. 15
E. 16

Bunuel · Accepted Answer

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.

Gonnaflynow · Answer

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!!

hfbamafan · Answer

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

cyberjadugar · Answer

Hi,

Firstly, 1/12*48 = 4

Secondly, You may find the correct question & solution here:
 https://gmatclub.com/forum/in-a-company-with-48-employees-some-part-time-and-some-full-132442.html

Regards,

shivanigs · Answer

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 :-D

Bunuel · Answer

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

Transcendentalist · Answer

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

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

vad3tha · Answer

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

EMPOWERgmatRichC · Answer

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

Final Answer:  D

GMAT assassins aren't born, they're made, 
Rich

roykabir772 · Answer

In the last step, it should be 36/12 + 48/4 = 15.

Cheers,
Kabir

energetics · Answer

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)

GMATinsight · Answer

Answer: Option D

Please check the video for the step-by-step solution.

GMATinsight's Solution

https://www.youtube.com/watch?v=68yHEhyIU1o

Fdambro294 · Answer

Just did simple Number Plugging.

The Q-Prompt says that some people work full-time, and some people work part-time. The inference is that there can not be 0 workers in either category.

Let P = No. of Part-time workers
Let F = No. of Full-Time Workers

Total No. of ppl who take the subway = 1/3 * P + 1/4 * F

Total No. of Workers = P + F = 48 *where P nor F can equal 0

Since the % of Part-Time workers who take subway > % of Full-Time workers who take the subway
Try to Maximize P and Minimize F

The Minimum No. of Full-Time Workers who take the subway = 1/4 * F must be a Multiple of 4. Also, the No. of Part-Time Workers who take the subway = 1/3 * P must be a Multiple of 3. You can not have a fractional person.

If F = 4, P = 44 (Not Divisible by 3)

If F = 8, P = 40 (Not Divisible by 3)

If F = 12, P = 36 (OK)

1/3 * (36) + 1/4 * (12) = 15 Total people who take the Subway.

Since it is not possible to get 16 people and 15 is higher than all of the rest of the Answer choices, D is Correct

bumpbot · Answer

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.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards