Hi All,
Before we get into this question, you've been posting a variety of 'tougher' prompts lately - so unless you're already scoring above 700 in your practice Exams (or on the Official GMAT), then you might be focusing on the wrong things.
In these types of 'rate' questions, it often helps to think in terms of the TOTAL work that must be done to complete the task. If a 24-man crew can complete the job in 16 days, then that means that (24)(16) = 384 man-days of effort are required to complete the job. If a 32-woman crew can complete the job in 24 days, then that means that (32)(24) = 768 woman-days of effort are required to complete the job.
Before we do anything else, it's important to compare these numbers: 384 and 768. Since 384 is exactly HALF of 768, in this question that means that the work that a woman does in 1 day = 1/2 of the work that a man does in 1 day.
We're told that 16 men and 16 women work for 12 days each. That means they complete....
(16 men)(12 days) = 192 man-days of work = 1/2 of the job gets done
(16 women)(12 days) 192 woman-days of work = 1/4 of the job gets done
1/2 + 1/4 = 3/4... so after 12 days, 3/4 of the job is done - and 1/4 of the job remains
We're going to add a certain number of men, so that the job is completed in 2 more days. First though, we have to figure out how much more of the job gets completed with the existing people during that time...
(16 men)(2 days) = 32 man-days of work = 1/12 of the job gets done
(16 women)(2 days) 32 woman-days of work = 1/24 of the job gets done
During the next 2 days, the existing people will complete 1/12 + 1/24 = 3/24 of the job gets done
That leaves us with 1/4 - 3/24 = 3/24 of the job remains. 3/24 of 384 man-days = 48 man-days of work. The extra men that will be added will work for 2 days each, so....
(X men)(2 days each) = 48 days of man-work
X = 24
Final Answer:
GMAT assassins aren't born, they're made,
Rich