A contractor estimated that his 10-man crew could complete : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 24 Jan 2017, 15:50

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A contractor estimated that his 10-man crew could complete

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: D-Day is on February 10th. and I am not stressed
Affiliations: American Management association, American Association of financial accountants
Joined: 12 Apr 2011
Posts: 270
Location: Kuwait
Schools: Columbia university
Followers: 5

Kudos [?]: 272 [1] , given: 52

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

### Show Tags

16 Jan 2012, 09:19
1
KUDOS
5
This post was
BOOKMARKED
00:00

Difficulty:

85% (hard)

Question Stats:

54% (03:04) correct 46% (02:13) wrong based on 135 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA

_________________

Sky is the limit

Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93662 [4] , given: 10583

Re: A contractor estimated that his 10-man [#permalink]

### Show Tags

16 Jan 2012, 12:07
4
KUDOS
Expert's post
manalq8 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

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.)

_________________
Manager
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 178
Location: India
WE: Information Technology (Investment Banking)
Followers: 3

Kudos [?]: 80 [0], given: 1

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

### Show Tags

17 Jan 2012, 02:16
Bunnel - Could you please explain the step
"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"
Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93662 [2] , given: 10583

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

### Show Tags

17 Jan 2012, 02:41
2
KUDOS
Expert's post
subhajeet wrote:
Bunnel - Could you please explain the step
"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"

10 men need 55 days to complete a job. How many days does 20 men need to complete the same job? In 55/2 days (the rate of 20 men group is twice the rate of 10 men group).

Similarly, if 10 men need 55 days to complete a job, 16 men (10*1.6) will need 55/1.6 days to complete the job (the rate of 16 men group is 1.6 times greater than the rate of 10 men group).

Or: there was 10*55=550 man-days of work left which can be done by 16 men in 550/16=~34.4 days.
Refer to two-consultants-can-type-up-a-report-126155.html for theory on work problems and practice questions.

Hope it helps.
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7132
Location: Pune, India
Followers: 2140

Kudos [?]: 13716 [1] , given: 222

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

### Show Tags

17 Jan 2012, 02:47
1
KUDOS
Expert's post
manalq8 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 also look at this problem in terms of units of work.

10 people can finish the work in 110 days so there are 1100 units of work (1 unit done by 1 man in 1 day)
10 men worked for 55 days and did 10*55 = 550 units (since it rained for 5 days so day 56th to day 60th were all washed out). Now 550 units are left. [Mind you, it is an assumption that there was no rain in the first 55 days. Ideally, the question should have explicitly stated it.)

Now there are 16 people to do 550 units of work. Work will be done in 550/16 = 34.4 days i.e. 35 days are needed.
After 60th day, we have total 40 days. Out of these, 35 are needed so it must have rained on 5 days.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Status: MBA Aspirant Joined: 12 Jun 2010 Posts: 178 Location: India Concentration: Finance, International Business WE: Information Technology (Investment Banking) Followers: 3 Kudos [?]: 80 [1] , given: 1 Re: A contractor estimated that his 10-man crew could complete [#permalink] ### Show Tags 17 Jan 2012, 02:51 1 This post received KUDOS Bunuel wrote: subhajeet wrote: Bunnel - Could you please explain the step "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" 10 men need 55 days to complete a job. How many days does 20 men need to complete the same job? In 55/2 days (the rate of 20 men group is twice the rate of 10 men group). Similarly, if 10 men need 55 days to complete a job, 16 men (10*1.6) will need 55/1.6 days to complete the job (the rate of 16 men group is 1.6 times greater than the rate of 10 men group). Or: there was 10*55=550 man-days of work left which can be done by 16 men in 550/16=~34.4 days. Refer to two-consultants-can-type-up-a-report-126155.html for theory on work problems and practice questions. Hope it helps. Bunnel thanks for your explanation. Manager Status: Trying.... & desperate for success. Joined: 17 May 2012 Posts: 78 Location: India Concentration: Leadership, Entrepreneurship Schools: NUS '15 GMAT 1: Q33 V27 GPA: 2.92 WE: Analyst (Computer Software) Followers: 0 Kudos [?]: 76 [0], given: 61 Re: A contractor estimated that his 10-man crew could complete [#permalink] ### Show Tags 20 Jul 2012, 09:45 VeritasPrepKarishma wrote: manalq8 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 also look at this problem in terms of units of work. 10 people can finish the work in 110 days so there are 1100 units of work (1 unit done by 1 man in 1 day) 10 men worked for 55 days and did 10*55 = 550 units (since it rained for 5 days so day 56th to day 60th were all washed out). Now 550 units are left. [Mind you, it is an assumption that there was no rain in the first 55 days. Ideally, the question should have explicitly stated it.) Now there are 16 people to do 550 units of work. Work will be done in 550/16 = 34.4 days i.e. 35 days are needed. After 60th day, we have total 40 days. Out of these, 35 are needed so it must have rained on 5 days. Thanks for letting kw the easy method. Intern Joined: 21 Sep 2010 Posts: 6 Followers: 0 Kudos [?]: 7 [0], given: 9 Re: A contractor estimated that his 10-man crew could complete [#permalink] ### Show Tags 20 Jul 2012, 11:22 I thought of the problem in units of work. The total project needed 1100 units of work. 550 of these units were completed by the 55th day (10 x 55). It rained on the 56th, 57th, 58th, 59th, and 60th day. On the 61st day, the contractor hired 6 more laborers thus bringing the total laborer population to 16. With 550 units of work left, these 16 laborers should have completed the remaining work in 34.375 days. Here's where I went wrong. I added 34.375 to 61 to bring total days needed (assuming no rain after the 60th) to 95.375 (essentially 96 days of work). However, this would imply only 4 days of rain since the project actually took 100 days to complete. I believe I went wrong in adding the 34.375 to 61 instead of 60 since by doing the former I didn't credit them for one day of work. Could someone confirm this? Thank you. Director Joined: 22 Mar 2011 Posts: 612 WE: Science (Education) Followers: 100 Kudos [?]: 894 [0], given: 43 Re: A contractor estimated that his 10-man crew could complete [#permalink] ### Show Tags 20 Jul 2012, 11:42 Club909 wrote: I thought of the problem in units of work. The total project needed 1100 units of work. 550 of these units were completed by the 55th day (10 x 55). It rained on the 56th, 57th, 58th, 59th, and 60th day. On the 61st day, the contractor hired 6 more laborers thus bringing the total laborer population to 16. With 550 units of work left, these 16 laborers should have completed the remaining work in 34.375 days. Here's where I went wrong. I added 34.375 to 61 to bring total days needed (assuming no rain after the 60th) to 95.375 (essentially 96 days of work). However, this would imply only 4 days of rain since the project actually took 100 days to complete. I believe I went wrong in adding the 34.375 to 61 instead of 60 since by doing the former I didn't credit them for one day of work. Could someone confirm this? Thank you. You are right. You simply took away one work day. The 61st day of the project was a work day, in fact the first day when the extended team of 16 took over the job. _________________ PhD in Applied Mathematics Love GMAT Quant questions and running. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7132 Location: Pune, India Followers: 2140 Kudos [?]: 13716 [0], given: 222 Re: A contractor estimated that his 10-man crew could complete [#permalink] ### Show Tags 20 Jul 2012, 18:19 Club909 wrote: I thought of the problem in units of work. The total project needed 1100 units of work. 550 of these units were completed by the 55th day (10 x 55). It rained on the 56th, 57th, 58th, 59th, and 60th day. On the 61st day, the contractor hired 6 more laborers thus bringing the total laborer population to 16. With 550 units of work left, these 16 laborers should have completed the remaining work in 34.375 days. Here's where I went wrong. I added 34.375 to 61 to bring total days needed (assuming no rain after the 60th) to 95.375 (essentially 96 days of work). However, this would imply only 4 days of rain since the project actually took 100 days to complete. I believe I went wrong in adding the 34.375 to 61 instead of 60 since by doing the former I didn't credit them for one day of work. Could someone confirm this? Thank you. Think of it this way: 60 days are accounted for. From the 61st day to the 100th day, there are 40 days. You need 35 of these to complete the work so you are left with 5 days. When you add 35 to 61, you are saying that 61 days are accounted for but that is not the case. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 25

Kudos [?]: 434 [0], given: 11

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

### Show Tags

14 Nov 2012, 06:30
$$\frac{10}{m}=\frac{1}{110}$$
$$rate=\frac{1}{1100}$$

10 men worked for 60-5=55 days...

$$\frac{10}{1100}(55)=\frac{55}{110}=\frac{1}{2}$$

How many remaining days required to finish with 16 men?

$$\frac{16}{1100}(t)=1/2==> t=34.3 days$$ is needed to finish the remaining work

To finish in 100 days or with the 40 days remaining, it should not rain for more than 5 days.

_________________

Impossible is nothing to God.

Intern
Joined: 01 Oct 2012
Posts: 18
Location: United States
Concentration: Entrepreneurship, Marketing
WE: Research (Energy and Utilities)
Followers: 0

Kudos [?]: 12 [0], given: 9

Re: A contractor estimated that his 10-man [#permalink]

### Show Tags

05 Jan 2013, 01:26
Bunuel wrote:
manalq8 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

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.)

Hi,

Estimated time = 110 days
actual completed time = 100 days
no work days = 110-100 = 10 days
we are given only rain is a factor because of which no work will be done and it has already rained for 5 days before the 60th. thus 10-5 = 5 more days it will rain after the 60th

why do we have get into work and rates for this?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7132
Location: Pune, India
Followers: 2140

Kudos [?]: 13716 [0], given: 222

Re: A contractor estimated that his 10-man [#permalink]

### Show Tags

05 Jan 2013, 01:39
geezer0305 wrote:
Hi,

Estimated time = 110 days
actual completed time = 100 days
no work days = 110-100 = 10 days
we are given only rain is a factor because of which no work will be done and it has already rained for 5 days before the 60th. thus 10-5 = 5 more days it will rain after the 60th

why do we have get into work and rates for this?

It took 100 days to complete the work instead of the estimated 110 because he employed 6 extra people, not because they did not work on those days. The workers actually worked for only 90 days. Out of the 100 days, it rained for 10 days and they worked for the rest of the 90 days. It is just a co-incidence that the extra workforce reduced the working days by 10, the same number of days for which it rained.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 19 Jul 2012 Posts: 22 Location: United States Concentration: Operations, Entrepreneurship Schools: INSEAD '14 WE: Consulting (Manufacturing) Followers: 0 Kudos [?]: 15 [0], given: 8 Re: A contractor estimated that his 10-man crew could complete [#permalink] ### Show Tags 14 Oct 2013, 11:09 Given 10 men took 110 days. Total work = 1100 Man Days Given on the 61-st day, after 5 days of rain, which means the 10 men worked for 55 days and completed: 55 X 10 = 550 Man Days of work. Remaining work = 1100-550 = 550 Man Days of work. Problem states that the work was completed early in 100 days by the 16 men. Assume it rained on x days, so the work was completed in 40-x days Hence , 16 (40-x)=550 or x ~ 5 days Hi, I wanted to understand if the above mentioned step in red is right. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7132 Location: Pune, India Followers: 2140 Kudos [?]: 13716 [0], given: 222 Re: A contractor estimated that his 10-man crew could complete [#permalink] ### Show Tags 14 Oct 2013, 22:49 chechaxo wrote: Given 10 men took 110 days. Total work = 1100 Man Days Given on the 61-st day, after 5 days of rain, which means the 10 men worked for 55 days and completed: 55 X 10 = 550 Man Days of work. Remaining work = 1100-550 = 550 Man Days of work. Problem states that the work was completed early in 100 days by the 16 men. Assume it rained on x days, so the work was completed in 40-x days Hence , 16 (40-x)=550 or x ~ 5 days Hi, I wanted to understand if the above mentioned step in red is right. Yes, but ensure that you understand how to deal with fractions. 16 (40-x)=550 40 - x = 34.375 x = 5.625 Now will you say it rained for 5 days or 6 days? Note that you will say that it rained for 5 days because the workers needed the extra .375 day to complete the work. If it were to rain on the 6th day too, the workers would not have been able to work on that day and hence the work would not be complete. The fraction means that on the 100th day, the workers worked i.e. there was no rain but they worked for only a fraction of the day because the work got over. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Re: A contractor estimated that his 10-man crew could complete   [#permalink] 14 Oct 2013, 22:49
Similar topics Replies Last post
Similar
Topics:
33 Pascal has 96 miles remaining to complete his cycling trip. 7 15 Dec 2013, 17:33
144 At his regular hourly rate, Don had estimated the labour cos 35 31 Jul 2012, 09:01
8 A contractor estimated that his 10-man crew could complete t 9 08 Jan 2011, 11:20
19 Crew A can build a complete car in 20 minutes and Crew B can build a 20 17 Apr 2010, 04:27
6 A work crew of 4 Men takes 5 days to complete one-half of a 10 13 Mar 2010, 08:24
Display posts from previous: Sort by