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# M07-06

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Math Expert
Joined: 02 Sep 2009
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15 Sep 2014, 23:34
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4
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Difficulty:

95% (hard)

Question Stats:

43% (01:58) correct 57% (02:52) wrong based on 138 sessions

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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. 4
B. 5
C. 6
D. 7
E. 8

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15 Sep 2014, 23:34
3
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Official Solution:

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

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 been 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-men crew needed $$\frac{55}{1.6} \approx 34.4$$ days to complete the construction, but after they were hired job was done in $$100-60=40$$ days. Therefore it rained for 5 days. (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.)

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13 Oct 2014, 18:49
Bunuel wrote:
Official Solution:

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

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 been 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-men crew needed $$\frac{55}{1.6} \approx 34.4$$ days to complete the construction, but after they were hired job was done in $$100-60=40$$ days. Therefore it rained for 5 days. (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.)

I was just curious, going by the complexity of the question as well as the explanation, is it really GMAT level? I mean i think it is way beyond it but i guess i might be missing something here.
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21 Oct 2014, 15:14
Hi Bunuel,

I solved this question as below.,

Let rate per worker be x

Rate Time Work

10x 110 1

10x 55 1/2

Let it rain for K days

16x (40-K) 1/2

so 16x(40-k) = 10x*55
which gives us 640x- 16Kx = 550x==> 16kx= 90x ==> K= 90/16 ==> 5.6 days.

Now I was confused whether to choose 5 or 6 since 5.6 is closer to 6.

But is my logic correct?

Regards,
Arun

earnit wrote:
Bunuel wrote:
Official Solution:

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

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 been 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-men crew needed $$\frac{55}{1.6} \approx 34.4$$ days to complete the construction, but after they were hired job was done in $$100-60=40$$ days. Therefore it rained for 5 days. (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.)

I was just curious, going by the complexity of the question as well as the explanation, is it really GMAT level? I mean i think it is way beyond it but i guess i might be missing something here.
Math Expert
Joined: 02 Sep 2009
Posts: 50627

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22 Oct 2014, 00:25
amariappan wrote:
Hi Bunuel,

I solved this question as below.,

Let rate per worker be x

Rate Time Work

10x 110 1

10x 55 1/2

Let it rain for K days

16x (40-K) 1/2

so 16x(40-k) = 10x*55
which gives us 640x- 16Kx = 550x==> 16kx= 90x ==> K= 90/16 ==> 5.6 days.

Now I was confused whether to choose 5 or 6 since 5.6 is closer to 6.

But is my logic correct?

Regards,
Arun

earnit wrote:
Bunuel wrote:
Official Solution:

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

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 been 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-men crew needed $$\frac{55}{1.6} \approx 34.4$$ days to complete the construction, but after they were hired job was done in $$100-60=40$$ days. Therefore it rained for 5 days. (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.)

I was just curious, going by the complexity of the question as well as the explanation, is it really GMAT level? I mean i think it is way beyond it but i guess i might be missing something here.

Rain = 5.6 and Work = 34.4.

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, which means that it rained for 5 days.
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09 Dec 2015, 02:04
5
Hi Bunnuel,

Kindly check my approach to this problem and pls comment on it:

Total Work = 10 persons X 110 days = 1100 person-days
Work completed till it rained for 5 days = 10 person X 55 days = 550 person-days.

Pending Work = 1100 - 550 = 550 person-days.
Ideally, from 61st day to 100th day, the manpower rose to 16, which means they can do a work of = 16 person X 40 days = 640 person-days.

But remaining work is only 550 person-days, so the difference is 640-550 = 90 person-days.
Therefore it rained for = 90/16 = 5.625 person-days.
Hence Work happened = 40-5.6 = 34.4 days

Hence it rained for 5 more days.

If u liked my detailed solution, a kudos will help
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09 Dec 2015, 02:48
Hi FightToSurvive !

Work completed till it rained for 5 days = 10 person X 55 days = 550 person-days.

How did you get 55 days here till it rained for 5 days starting form 61st day?
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15 Dec 2015, 09:49
1
1
one man completes 1/1100 of total job in one day
(10)(55)/1100=1/2 of job
d=days to complete remaining 1/2 of job,
16d/1100=1/2
d=34.4 working days
40 total days taken-34.4 working days=5.6 rain days
can't round rain days up to 6 without exceeding 100 total days for job
Senior Manager
Joined: 31 Mar 2016
Posts: 386
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)

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30 Aug 2016, 04:05
I think this is a high-quality question and I agree with explanation.
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Joined: 07 Dec 2016
Posts: 2

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24 Dec 2016, 15:53
2
Total Estimate for total Man days = 110 days x 10 Men = 1,100 Man days
Total Actual = 55 days x 10 Men = 550 Man days
Total remaining Man days = Total Est. - Total actual = 1,100 - 550 = 550 remaining Man days

Total days needed to complete the job = Remaining Man days / Total workers = 550/16 = 35 days (However, question stated that they took 40 days instead)
Rain days = 40 (Given)- 35 = 5 days

Hope this helped.

A&N
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Joined: 17 May 2016
Posts: 29
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12 Jan 2017, 04:42
Hi,

It may sound idiot and I apologies first for it,

How do you quickly calculate that $$\frac{550}{16} = 34,4$$ ?

In GMAT there are lot of intermediate calculus like this one that makes me lose lot of time and I do not know how to go fast on them

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Joined: 02 Sep 2009
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12 Jan 2017, 05:55
nickimonckom wrote:
Hi,

It may sound idiot and I apologies first for it,

How do you quickly calculate that $$\frac{550}{16} = 34,4$$ ?

In GMAT there are lot of intermediate calculus like this one that makes me lose lot of time and I do not know how to go fast on them

$$\frac{550}{16}$$

Reduce by 2: $$\frac{275}{8}$$. Next you should simply divide 275 by 8.
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26 Feb 2017, 19:59
Bunuel wrote:
Official Solution:

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

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 been working for 55 days thus completed $$\frac{1}{2}$$ of the job, $$\frac{1}{2}$$ 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-men crew needed $$\frac{55}{1.6} \approx 34.4$$ days to complete the construction, but after they were hired job was done in $$100-60=40$$ days. Therefore it rained for 5 days. (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.)

Dear Bunuel, How could we relate the people hired to the speed of construction?

$$Rate = \frac{1}{Time}$$
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27 Feb 2017, 03:27
AustinKL wrote:
Bunuel wrote:
Official Solution:

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

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 been working for 55 days thus completed $$\frac{1}{2}$$ of the job, $$\frac{1}{2}$$ 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-men crew needed $$\frac{55}{1.6} \approx 34.4$$ days to complete the construction, but after they were hired job was done in $$100-60=40$$ days. Therefore it rained for 5 days. (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.)

Dear Bunuel, How could we relate the people hired to the speed of construction?

$$Rate = \frac{1}{Time}$$

Let me ask you: say 1 man can do a certain job in 10 hours. In how many hours can the job be done by 2 men? In 5 hours, right. So, increasing the number of men twice we reduce the time need by the same rate.
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24 Jun 2017, 00:14
I did it this way and i derived at the right answer as well.

Total work done 110x10=1110

55 days work= 55x10=550.

5 days rain=zero work done

61st day 16 works are working. Work is completed in 100 days. So remaining work done in days is 550/16 is approximaterly 34.xx and round off to the next largest integer 35. So 100-55-5-35=5 days.
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10 Oct 2017, 18:25
Hi Bunuel,

I think this is a good question, but one thing needs to be clarified. Semantically, it is unclear from the question stem whether the job was completed 100 days from when it was started (regardless of how many days the workers did or did not work), or it was completed in 100 working days (instead of 110).

Personally, that confused me for long enough to make me guess and move on.

Thanks!
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06 Jul 2018, 13:21
1
This came towards the end of my CAT - given the complexity of the question, I just skipped it...
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30 Aug 2018, 08:55
Short and logical Approach:

(10 man-crew X 110 Days) = 1100 Man-days
Less: (10 man-crew X 55 days (On 61st day, 5 rainy days are already passed.)) = 550 Man-days
Balance Work = 550 Mandays

Total man-crew from 61st day=10+6=16
Hence, Balance work after 60 days will be divided by 16 man-crew to arrive at no of days worked after 60th day.
=550/16 = Appx. 35 days worked appx. (Remember we need to consider part of the day as full day)
Hence, 100 days-60 days = 40 days
40 days-35 days worked=5 rainy days after 60th day.
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Hope it's clear.
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11 Sep 2018, 00:58
Hi Bunnuel,

Kindly check my approach to this problem and pls comment on it:

Total Work = 10 persons X 110 days = 1100 person-days
Work completed till it rained for 5 days = 10 person X 55 days = 550 person-days.

Pending Work = 1100 - 550 = 550 person-days.
Ideally, from 61st day to 100th day, the manpower rose to 16, which means they can do a work of = 16 person X 40 days = 640 person-days.

But remaining work is only 550 person-days, so the difference is 640-550 = 90 person-days.
Therefore it rained for = 90/16 = 5.625 person-days.
Hence Work happened = 40-5.6 = 34.4 days

Hence it rained for 5 more days.

If u liked my detailed solution, a kudos will help

Hi Bunuel, FightToSurvive

I also did some similar to the above as it's simpler than the official solution.
But in the end, we get that it rained for 5.6 days.
And question says team doesn't work on the day it rains. so even if it rained 0.6 of a day, the team wouldn't work on that day.
so ultimately, this approach gives the ans as 6 days of rain which is wrong.

Can you please confirm if the above method is correct? IF yes, then how can it be used to get the ans.

Thanks.
Re: M07-06 &nbs [#permalink] 11 Sep 2018, 00:58
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# M07-06

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