A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?
A. 4
B. 5
C. 6
D. 7
E. 8
OA: 5
source: GMATclub test
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Difficult work problem
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DavidG@VeritasPrep
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Call the rate for one man 'r.' The rate for 10 men would be 10r. If those 10 men can do 1 job in 110 days, then we know that 10r = 1/110, and r = 1/1100Mo2men wrote:A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?
A. 4
B. 5
C. 6
D. 7
E. 8
OA: 5
source: GMATclub test
If 61st day follows 5 days of rain, then the workers work for 55 days, meaning they've finished half the job. (55 is 1/2 of 110.)
After 6 more workers are hired, there will be 16 workers. If r = 1/1100, then 16 workers will have a rate of 16/1100 = 4/275. Call the number of days they actually work "t." The amount of the job they'll have done will be (4/275) * t. If this constitutes 1/2 of the job then (4/275) * t = 1/2; t = 275/8; t = 34 3/8, so there are 35 days on which they work.
Between the 61st and the 100th day, there will be a total of 40 days. If they do work on 35 out of the 40 remaining days, it will have rained on 5 of them. The answer is B
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Let the rate for each worker = 1 widget per day, implying that the rate for 10 workers = 10 widgets per day.Mo2men wrote:A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?
A. 4
B. 5
C. 6
D. 7
E. 8
Since the job can be finished in 110 days, the total job = (rate for 10 workers)(total number of days) = 10*110 = 1100 widgets.
Since the first 60 days include 5 days of rain, work is produced on 55 of the first 60 days.
Thus, the number of widgets produced in the first 60 days = (rate for 10 workers)(number of work-days) = 10*55 = 550.
Remaining number of widgets = (total job) - (work produced in the first 60 days) = 1110-550 = 550 widgets.
Since the job is completed in 100 days, the remaining number of days = (total number of days) - (first 60 days) = 100-60 = 40 days.
After 6 workers are hired, the rate increases to 16 widgets per day.
Time for 16 workers to produce the remaining 550 widgets = w/r = 550/16 = 34 3/8 days.
The value in blue indicates that -- for the job to be completed -- widgets must be produced on 35 of the remaining 40 days.
Thus, the number of rainy days after the first 60 days = (total number of remaining days) - (total number of remaining work-days) = 40-35 = 5.
The correct answer is B.
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Creative alternative:
We know that rate and time have a reciprocal relationship. When we add 6 men to the existing 10, we're increasing the number of workers, and therefore the rate, by 60% or 3/5. To increase something by 3/5 is the same as multiplying that value by 8/5.
If we're multiplying the rate by 8/5, it means we're multiplying the time by the reciprocal, or 5/8. If the first half of the job (with 10 workers) required 55 days, the second half (with 60% more workers) will require 55 * 5/8 = 275/8 = 34 3/8 days, or 35 work days, leaving 5 of the last 40 days for rain.
We know that rate and time have a reciprocal relationship. When we add 6 men to the existing 10, we're increasing the number of workers, and therefore the rate, by 60% or 3/5. To increase something by 3/5 is the same as multiplying that value by 8/5.
If we're multiplying the rate by 8/5, it means we're multiplying the time by the reciprocal, or 5/8. If the first half of the job (with 10 workers) required 55 days, the second half (with 60% more workers) will require 55 * 5/8 = 275/8 = 34 3/8 days, or 35 work days, leaving 5 of the last 40 days for rain.
Last edited by DavidG@VeritasPrep on Thu Mar 02, 2017 7:52 am, edited 1 time in total.
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Hi Mo2men,
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 10-man crew can complete the job in 110 days, then that means that (10)(110) = 1100 worker-days of effort are required to complete the job. That could be 1 worker working 1100 days, 2 workers working 550 days each, 2 workers working for 100 days and 90 other workers working for 10 days, etc.
We're told that there were 5 days of rain in the first 60 days, so the 10 workers worked for 55 days = (10)(55) = 550 worker-days of the 1100 required were completed. From that point on, there were 16 workers on the job each day; we can calculate how many days it would take those 16 workers to complete the task:
550/16 = 275/8 = 34 3/8 days needed to complete the job
We're told that the job was completed on day 100. Since that time period includes 100 - 60 = 40 days, and 35 (rounded up) days were needed to complete the work, then then 40 - 35 = 5 days were lost during that time due to rain.
Final Answer: B
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Rich
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 10-man crew can complete the job in 110 days, then that means that (10)(110) = 1100 worker-days of effort are required to complete the job. That could be 1 worker working 1100 days, 2 workers working 550 days each, 2 workers working for 100 days and 90 other workers working for 10 days, etc.
We're told that there were 5 days of rain in the first 60 days, so the 10 workers worked for 55 days = (10)(55) = 550 worker-days of the 1100 required were completed. From that point on, there were 16 workers on the job each day; we can calculate how many days it would take those 16 workers to complete the task:
550/16 = 275/8 = 34 3/8 days needed to complete the job
We're told that the job was completed on day 100. Since that time period includes 100 - 60 = 40 days, and 35 (rounded up) days were needed to complete the work, then then 40 - 35 = 5 days were lost during that time due to rain.
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
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Jay@ManhattanReview
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Hi Mo2men,Mo2men wrote:A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?
A. 4
B. 5
C. 6
D. 7
E. 8
OA: 5
source: GMATclub test
Here's one more take on the Work/Rate PS question.
We know that 61st day (No-rain day) falls after the five days of rain. It means that the 10-men crew worked for 60 - 5 = 55 days. Since the crew can complete the work in 110 days, in 55 days, it completed half the work. Or, 55 days of work is remaining.
Since on 61st day, the contractor hired 6 more people, thus if there is no rain after the 60th day, the 16-men crew would complete the remaining work in 55*(10/16) days.
But we know that the remaining work was completed in 100 - 60 - another stretch of rainy days = 40 - rainy days
Say # of rainy days = x.
Thus, 55*(10/16) = 40 - x
=> x = 45/8 = 5.625 days.
Mathematically speaking, we must round up 5.625 to get the integer value 6, but this would leave some of the work and the remaining work would not be completed in 100 days. Thus, we would round down 5.625 to 5 days.
It rained for 5 days after the 60th day.
The correct answer: B
Hope this helps!
Relevant book: Manhattan Review GMAT Word Problems Guide
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Just as a footnote, these GMATClub questions can be pretty artless. (Not all of them, some of them are nice, but too many of them tend to be hard, out of scope, or tedious.) The problems on the actual exam don't tend to involve this much computational drudgery, so if you get bogged down on this, don't sweat it too much.
