gmat_guy666 wrote:A contractor hires 100 men to finish a job in 50 days. After 14 days, n men leave. After some more days, the contractor hires 2n more men to complete the job on time. For how many days did these 2n men work?
A. 20
B. 18
C. 16
D. 12
E. 8
Let the rate for each man = 1 unit per day.
Rate for 100 men = 100 units per day.
In 50 days, the amount of work produced by all 100 men = 100*50 = 5000 units.
This is the value of the job.
In 14 days, the amount of work produced by 100 men = 100*14 = 1400 units.
Remaining work = 5000-1400 = 3600 units.
Since the job is finished on time, the remaining amount of time after 14 days = 50-14 = 36 days.
Let n = 50, implying that 100-50 = 50 men for a certain number of days and that 100+50 = 150 men work for the remaining number of days.
We can PLUG IN THE ANSWERS, which represent the number of days worked by the 150 men.
When the correct answer is plugged in, the remaining 3600 units will be completed in 36 days.
Answer choice D: 12 days for the 150 men, implying 24 days for the 50 men
Amount of work produced by 50 men in the first 24 days and by 150 men in the remaining 12 days = (50*24) + (150*12) = 1200 + 1800 = 3000.
Too little work is produced, implying that the 150 men must work for LONGER.
Eliminate D and E.
Answer choice B: 18 days for the 150 men, implying 18 days for the 50 men
Amount of work produced by 50 men in the first 18 days and by 150 men in the remaining 18 days = (50*18) + (150*18) = (50+150)(18) = 200*18 = 3600.
Success!
The correct answer is
B.
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