Problem Solving

Jack needs workers to clean his driveway for the current season. Each worker costs $4000/month. The current season has 5 months, and Jack is willing to hire 150 workers per season. What will be the cost per season incurred by Jack?

A $600K
B $120K
C $300K
D $200K
E $100K

OA A
Source - GMAT Book by Kaplan/Princeton (I forgot)

I am not sure how I can represent current wage -- is it $4000/month/person or $4000/person/month or $4000/(person * month). Here's why:

Case (i) Wage = $4000/month/person

150 people are hired in one season, and there are 5 months in one season.

Therefore #of months/person = 5 month/season * 1 season/150 person = 1 month / 30 person.

Therefore, total cost = $4000/(month/person) * 1 month / 30 person = $4000/30 (What will be the unit? I believe "$")

Case (ii) Wage = $4000/(month*person)
Therefore total cost =$4000/(month*person) * 5 months/ season * 150 people / season = $4000*5*150 / season = $3000K / season (what will be the unit? 1/season^2?)

Case (iii) Wage = $4000/person/month
Therefore total cost = $4000 / person / month * (150 person / season) * (1 season/month) = $120K (units = $/(month)^2?? or $/month?) I really confused. Therefore, total cost per season = $120K * 5 = $600K

I am not sure which case is correct/incorrect and why. I would appreciate any help.

Thanks

[email protected] wrote:Hi voodoo_child,

I think that there's at least 1 typo in this question. Since you can't remember the source, then how did you transcribe this prompt?

This is essentially a "rate" question, so you should organize it in whichever way is easiest for you.

Let's start with 1 worker....

1 worker = $4,000/month
1 worker = $20,000/5 months

150 workers for 5 months --> (150)($20,000) = $3,000,000

Since this answer is not among the answer choices, either the prompt has typos or the answer choices have typos.

If Jack hired 30 workers (instead of the 150 that are listed in the prompt), then the cost would be $600,000. I only bring this up because in one of your "possible explanations", you reference 30 workers (and not 150).

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

Rich,
Thank you so much for your response. Here's the official text. I wroted this question in my notes and lost the original book while moving. However, I do have the notes. Here's the exact text about wages.

"Jack will need to hire 150 people for the whole season, but the actual number of workers per month varies and can get as high as 60. Jack will have to pay workers for the whole month, even if he needs them only for one week. Each worker costs $4,000 / month, and there are 5 months in the season."

I think the author is saying that Jack can hire only 150 workers in 5 months, which averages to 30 workers in one month.
I generally convert the hourly wages to the form $X / person / time-frame. For instance, $x/person/hours etc. However, I was a bit lost in this question because I could have three possible scenarios highlighted above.
Could it be $X/ (time * person), OR $X / person/time OR $x/time/person. I am a bit lost. In each of these cases, I got a different answer. Moreover, the units are all over the place i.e. 1/month^2 or even 1/season^2. I am not really sure.

I would appreciate if you could clarify this for me. I look forward to hearing from you.

Thanks in advance.