Why are there only 4 answer choices? Also we don't know whether all persons have the same work rate, so this is technically unsolvable. Not a valid GMAT question!
Assuming that each person has the same rate, we can solve.
Work equation is work=rate*time.
It takes 8 people 12 days to do 1/4 of work. If r is the rate of each person we can write work=rate*time >> (1/4)=(8r)(12) >> r=(1/4)(1/96) (don't spend the time to calculate it here).
We want to know how many people are needed to do 3/4 of work (what remains) in 16 days. Since work=rate*time, we can write (3/4)=(p*r)(16) where p is the number of people needed and r=(1/4)(1/96)
Solving for p gives you p=18 people needed. Please check that you have correctly copied the correct answer choices.
A DIFFERENT APPROACH
It takes 8 ppl 12 days to do a 1/4 of the work, so it would take them 36 days (3 times as long) to do the remaining 3/4 of the work.
We want the remaining 3/4 work to take only 16 days but it would take the 8 ppl 36 days (3 times as long) to do this job. Time and rate are inversely proportional. To decrease the required time from 36 to 16, the initial 36 days were multiplied by 16/36 = 4/9. The corresponding change needed in the rate is a multiplication by 9/4. So if there were 8 people to begin with, we will need 8 * (9/4) = 18 people to meet the 16 day deadline.
Again the answer is 18. The answer choices provided are way too low.
If you are looking for reliable, hard rate questions, use the Solutions Engine to go through GMATPrep questions. Set topic='Work & Rate' and difficulty='700+' in the Drill Generator
-Patrick
Last edited by
Patrick_GMATFix on Sat Jul 17, 2010 11:35 am, edited 3 times in total.
