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A contractor estimated that his 10-man crew could complete t [#permalink]

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08 Jan 2011, 11:20

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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 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?

4 5 6 7 8

Given: 10-man crew needs 110 days to complete the construction.

"On the 61-st day, after 5 days of rain ..." --> as it was raining for 5 days then they must have bee working for 55 days thus completed 1/2 of the job, 1/2 is left (55 days of work for 10 men).

Then contractor "hired 6 more people" --> speed of construction increased 1.6 times, so the new 16-man crew needed 55/1.6=~34.4 days to complete the construction, but after they were hired job was done in 100-60=40 days --> so 5 days rained. (They needed MORE than 34 days to finish the job, so if it rained for 6 days they wouldn't be able to finish the job in 100(40) days.)

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?

4 5 6 7 8

You can visualize it in another way: 10 man crew needs 110 days means the total work = 10*110 = 1100 man-days (man-days means the amount of work 1 man does in 1 day)

In 60 days, it rained for 5 days and the crew worked for 55 days and completed 10*55 = 550 man-days work and left over work is 1100 - 550 = 550 man-days

From 61st day on, there are 16 people working and will need 550/16 = 34.4 days to complete the remaining work. So out of 40 days (from 61st to 100th day), 35 days were used (though the 100th day wasn't completely utilized) and it must have rained on 5 days.
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From 61st day on, there are 16 people working and will need 550/16 = 34.4 days to complete the remaining work. So out of 40 days (from 61st to 100th day), 35 days were used (though the 100th day wasn't completely utilized) and it must have rained on 5 days.

your method makes sense, but i got kind of lost at the end. so if it takes 34.4 days, wouldn't it be 61+34=95 days, so it rained for 5 days? thanks.

From 61st day on, there are 16 people working and will need 550/16 = 34.4 days to complete the remaining work. So out of 40 days (from 61st to 100th day), 35 days were used (though the 100th day wasn't completely utilized) and it must have rained on 5 days.

your method makes sense, but i got kind of lost at the end. so if it takes 34.4 days, wouldn't it be 61+34=95 days, so it rained for 5 days? thanks.

Yes it rained on 5 days but the job took 34.4 days, so more than 34 (full 34 days and the part of 35th day). Next, you should count from 61st day (61st day is the first day when 16 men crew started to work) so 60+35=95 (not 61+...) --> 100-95=5.
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From 61st day on, there are 16 people working and will need 550/16 = 34.4 days to complete the remaining work. So out of 40 days (from 61st to 100th day), 35 days were used (though the 100th day wasn't completely utilized) and it must have rained on 5 days.

your method makes sense, but i got kind of lost at the end. so if it takes 34.4 days, wouldn't it be 61+34=95 days, so it rained for 5 days? thanks.

As bunuel pointed out above, it rained for 5days in the first 60 days. Thereafter, in the remaining 100 - 60 = 40 days, they worked for 34.4 days ie 35 days (the 35th day, they worked partly). The rest of the 5 days, it rained. Snce the work was not over in 34 days, they needed the 35th day. You cannot round it off to 34.
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Re: A contractor estimated that his 10-man crew could complete t [#permalink]

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15 Oct 2014, 08:49

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Re: A contractor estimated that his 10-man crew could complete t [#permalink]

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19 Oct 2014, 06:41

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110 days * 10 workers= 1100 units of work in total..

55 days of work done with help of 10 workers..therefore, 55 days * 10 workers = 550 units of work done..it means 550 units of work remaining..

It means, 550 units /16 workers = 34.3 days required to finish the work..

Since the work done in 100 days,we have 40 days remaining, but the days required are 34.3 or we can say 35 since,until 0.3 units of work is not completed,we cannot claim that work is completed..

Hence 5 days of work remain...

Hope it helps..
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Re: A contractor estimated that his 10-man crew could complete t [#permalink]

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03 Jun 2016, 05:08

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A contractor estimated that his 10-man crew could complete t [#permalink]

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03 Jun 2016, 05:44

rtaha2412 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

10 men worked for 55 days. It rained from 56th to 60th day. On 61st day, he hired 6 more people, making total 16 people working.

Since 10 men can complete total work in 110 days, they must have completed 1/2 work in first 55 days.

From day 61 he had 16 workers working in remaining 1/2 work.

Now, if 10 workers take 55 days to complete 1/2 work, 16 workers take 55*10/16= 34.3 days (34 days + next day= 35 days) But its given that they finished the work in 40 days (61st to 100th day). Hence they did not work on 40-35= 5 days

B is the answer
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Re: A contractor estimated that his 10-man crew could complete t [#permalink]

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04 Dec 2017, 23:47

VeritasPrepKarishma wrote:

rtaha2412 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?

4 5 6 7 8

You can visualize it in another way: 10 man crew needs 110 days means the total work = 10*110 = 1100 man-days (man-days means the amount of work 1 man does in 1 day)

In 60 days, it rained for 5 days and the crew worked for 55 days and completed 10*55 = 550 man-days work and left over work is 1100 - 550 = 550 man-days

From 61st day on, there are 16 people working and will need 550/16 = 34.4 days to complete the remaining work. So out of 40 days (from 61st to 100th day), 35 days were used (though the 100th day wasn't completely utilized) and it must have rained on 5 days.

Following your approach, I did this, but the answer came out wrong.

after 60 days have passed, the 16 member crew is able to do 550 mandays of work in 40 days.

What would've happened if it worked for the 40 days? they would have done 640 mandys of work. But they did only 550 mandays of work. so they did not work for the number of days it would have taken them to do 640-550 = 90 mandays of work

90/16 = 5.625 rounding off gives 6!
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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?

4 5 6 7 8

You can visualize it in another way: 10 man crew needs 110 days means the total work = 10*110 = 1100 man-days (man-days means the amount of work 1 man does in 1 day)

In 60 days, it rained for 5 days and the crew worked for 55 days and completed 10*55 = 550 man-days work and left over work is 1100 - 550 = 550 man-days

From 61st day on, there are 16 people working and will need 550/16 = 34.4 days to complete the remaining work. So out of 40 days (from 61st to 100th day), 35 days were used (though the 100th day wasn't completely utilized) and it must have rained on 5 days.

Following your approach, I did this, but the answer came out wrong.

after 60 days have passed, the 16 member crew is able to do 550 mandays of work in 40 days.

What would've happened if it worked for the 40 days? they would have done 640 mandys of work. But they did only 550 mandays of work. so they did not work for the number of days it would have taken them to do 640-550 = 90 mandays of work

90/16 = 5.625 rounding off gives 6!

The answer is the same - you need to use logic here to figure out whether you will round off to 5 or 6. Note that in my explanation above, I rounded off 34.4 days to 35 days. Why? Because they worked for a part of the 35th day too. The work got completed in 0.4 day but the 35th day was used. Hence it rained for 5 days only. You will use the same logic. 5.6 days were not used. It must have rained on 5 days and a part of the 6th day must have been used so it must not have rained on it.
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Re: A contractor estimated that his 10-man crew could complete t [#permalink]

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05 Dec 2017, 00:31

Hi VeritasPrepKarishma, thank you for the prompt response. I understand your point. But considering what you have said, it would be needed to be specified by the question that if it rains for a portion of a day, the remaining time is used by the workers and that counts as a full day of work.

Hi VeritasPrepKarishma, thank you for the prompt response. I understand your point. But considering what you have said, it would be needed to be specified by the question that if it rains for a portion of a day, the remaining time is used by the workers and that counts as a full day of work.

Posted from my mobile device

No. The question tells you - "Assume the crew does not work on any rainy day "

They worked partially on the last day because the work got over, not because it rained.
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Re: A contractor estimated that his 10-man crew could complete t [#permalink]

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05 Dec 2017, 00:44

VeritasPrepKarishma wrote:

ShashankDave wrote:

Hi VeritasPrepKarishma, thank you for the prompt response. I understand your point. But considering what you have said, it would be needed to be specified by the question that if it rains for a portion of a day, the remaining time is used by the workers and that counts as a full day of work.

Posted from my mobile device

No. The question tells you - "Assume the crew does not work on any rainy day "

They worked partially on the last day because the work got over, not because it rained.

Got it. Thanks a lot for your help. Also, is this an official question? what's the source? because I have seen this question in my CAT prep material somewhere.