duahsolo 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
This is VERY similar to this Official Guide question:
https://www.beatthegmat.com/og-help-problem-t286349.html
The important thing here to recognize here is that the number of part-time employees and the number of full-time employees must be positive INTEGERS. For example, we can't have 5 1/3 part-time employees.
Also recognize that we're told that we have
some part-time and some full-time employees
Since "some" means 1 OR MORE, we cannot have zero part-time employees or zero full-time employees.
Okay, now onto the question...
We want to MAXIMIZE the number of employees who take the subway to work.
Since a greater
proportion of part-time employees take the subway to work, we want to MAXIMIZE the number of PART-time employees in the class.
The greatest number of part-time employees is 47 (since 48 part-time employees would mean 0 full-time employees, and we must have at least 1 full-time employee)
47 part-time employees
This is no good, because 1/3 of the part-time employees take the subway to work, and 47 is not divisible by 3.
So, let's try ...
46 part-time employees
This is no good, because 1/3 of the part-time employees take the subway to work, and 46 is not divisible by 3.
As you can see, we need only consider values where the number of part-time employees is divisible by 3. So, that's what we'll do from here on...
45 part-time employees
If 1/3 of the part-time employees take the subway to work, then 15 part-time employees take subway. Fine.
HOWEVER, if there are 45 part-time employees, then there must be 3 full-time employees .
If 1/4 of the full-time employees take the subway to work, then there can't be 3 full-time employees, since 3 is not divisible by 4.
42 part-time employees
This means there are 6 full-time employees
If 1/4 of the full-time employees take the subway to work, then there can't be 6 full-time employees, since 6 is not divisible by 4.
39 part-time employees
This means there are 9 full-time employees
If 1/4 of the full-time employees take the subway to work, then there can't be 9 full-time employees, since 9 is not divisible by 4.
36 part-time employees and 12 full-time employees
1/3 of the part-time employees take the subway to work, so
12 part-time employees walk
1/4 of the full-time employees take the subway to work, so
3 full-time employees walk
PERFECT - it works!!
So, a total of
15 employees take the subway to work
Answer:
D
Cheers,
Brent
