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

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

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,

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

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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

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

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:

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

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

Cheers,
Kabir

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)

Answer: Option D

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

GMATinsight's Solution

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

Hi Bunuel, I like your approach. If we were looking for the minimum, would it be (12/12)+12 = 1+12 = 13 ?

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