November 22, 2018 November 22, 2018 10:00 PM PST 11:00 PM PST Mark your calendars  All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA) November 24, 2018 November 24, 2018 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50730

A contractor undertakes to do a job within 100 days and hires 10 peopl
[#permalink]
Show Tags
09 Sep 2015, 01:11
Question Stats:
70% (02:21) correct 30% (02:39) wrong based on 608 sessions
HideShow timer Statistics




CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2702
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: A contractor undertakes to do a job within 100 days and hires 10 peopl
[#permalink]
Show Tags
09 Sep 2015, 10:16
Bunuel wrote: A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?
(A) 60 (B) 70 (C) 75 (D) 80 (E) 100
Kudos for a correct solution. CONCEPT: \(\frac{(Machine_Power * Time)}{Work} = Constant\)i.e. \(\frac{(M_1 * T_1)}{W_1} = \frac{(M_2 * T_2)}{W_2}\) In 10 workers finish 1/4 work in 20 days Remaining work = 1(1/4) = 3/4 No. of People left to work = 10(total)  2(fired) = 8 Days left = ? \(\frac{(10 * 20)}{(1/4)} = \frac{(8 * T_2)}{(3/4)}\) i.e. \(T_2 = 75\) Days Answer: option C
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION




Manager
Joined: 10 Aug 2015
Posts: 103

Re: A contractor undertakes to do a job within 100 days and hires 10 peopl
[#permalink]
Show Tags
09 Sep 2015, 03:54
Solution: Let the work done by one person per day be x Then, work done by 10 persons per day is 10x. work done by 10 persons in 20 days is 20*10x which is equal to 1/4th of total work. Therefore, x = 1/800. Work done by 8 persons in n days(n*8x) is 3/4th of total work. Therefore, n = 3/32x = 2400/32 = 75.
Option, C




Director
Joined: 21 May 2013
Posts: 653

Re: A contractor undertakes to do a job within 100 days and hires 10 peopl
[#permalink]
Show Tags
09 Sep 2015, 03:59
Bunuel wrote: A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?
(A) 60 (B) 70 (C) 75 (D) 80 (E) 100
Kudos for a correct solution. (10 people*20 days)/1/4=(8*x)/3/4 Solving for x, x=75 Answer C



Manager
Joined: 27 Aug 2014
Posts: 140
Concentration: Finance, Strategy
GPA: 3.9
WE: Analyst (Energy and Utilities)

Re: A contractor undertakes to do a job within 100 days and hires 10 peopl
[#permalink]
Show Tags
09 Sep 2015, 13:33
Bunuel wrote: A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?
(A) 60 (B) 70 (C) 75 (D) 80 (E) 100
Kudos for a correct solution. Answer is C. Total work content = 100*10 = 1000[units] work done in 20 days by 10 people = 250[units] 20 days  250[units] 10[people] x days  750[units]  8[people] x = 20*(750/250)*(10/8) = 75[days] C



Current Student
Status: GMAT Date: 10/08/15
Joined: 17 Jul 2014
Posts: 87
Location: United States (MA)
Concentration: Human Resources, Strategy
GPA: 3.5
WE: Human Resources (Consumer Products)

Re: A contractor undertakes to do a job within 100 days and hires 10 peopl
[#permalink]
Show Tags
10 Sep 2015, 09:02
Step 1: 1/4 of the work was done in 20 days So, complete work will be done in 20*4 = 80 days.From the question stem  10 people are hired to complete a job within 100 days  now we know they will finish this in 80 days. Step 2: As 20 day's work is already done, only 60 days of work remains. We know that 2 people have been fired, so we can use unitary method to solve the number of days required: People working  days required to complete 3/4 of the work 10  60 1  60/10 8  60*8/10 = 75Option C
_________________
Thanks, aimtoteach
~~~~~~~~~~~~~~~~~
Please give Kudos if you find this post useful.



Manager
Joined: 29 Jul 2015
Posts: 158

Re: A contractor undertakes to do a job within 100 days and hires 10 peopl
[#permalink]
Show Tags
10 Sep 2015, 09:15
Bunuel wrote: A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?
(A) 60 (B) 70 (C) 75 (D) 80 (E) 100
Kudos for a correct solution. Work done by 10 people in 10 days = 1/4 Work to be completed by 8 people = 3/4 Let x be the time taken by 8 people to complete 3/4 work. Then, at constant rate R \(\frac{M_1RT_1}{W1}\) = \(\frac{M_2RT_2}{W2}\) or \(\frac{20*10*R}{\frac{1}{4}} = \frac{x*8*R}{\frac{3}{4}}\) or x= 75 Answer: C



Math Expert
Joined: 02 Sep 2009
Posts: 50730

Re: A contractor undertakes to do a job within 100 days and hires 10 peopl
[#permalink]
Show Tags
13 Sep 2015, 07:29
Bunuel wrote: A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?
(A) 60 (B) 70 (C) 75 (D) 80 (E) 100
Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTION:Can we say that 10 people can finish the work in 100 days? No. If that were the case, after 20 days, only 1/5th of the work would have been over. But actually 1/4th of the work is over. This means that ‘10 people can complete the work in 100 days’ was just the contractor’s estimate (which turned out to be incorrect). Actually 10 people can do 1/4th of the work in 20 days. The contractor fires 2 people. So the question is how many days are needed to complete 3/4th of the work if 8 people are working? We need to find the number of days. How is ‘no. of days’ related to ‘no. of people’ and ‘work done’? If we have more ‘no. of days’ available, we need fewer people. So ‘no. of days’ varies inversely with ‘no. of people’. If we have more ‘no. of days’ available, ‘work done’ will be more too. So ‘no. of days’ varies directly with ‘work done’. Therefore, ‘no. of days’ * ‘no. of people’/’work done’ = constant \(20*\frac{10}{(\frac{1}{4})} =\) ‘no. of days’*\(\frac{8}{(\frac{3}{4})}\) No. of days = 75 So, the work will get done in 75 days if 8 people are working. We can also do this question using simpler logic. The concept used is joint variation only. Just the thought process is simpler. 10 people can do 1/4th of the work in 20 days. 8 people can do 3/4th of the work in x days. Start with the no. of days since you want to find the no of days: \(x = 20*(\frac{10}{8})*(\frac{3}{1}) = 75\) From where do we get 10/8? No. of people decreases from 10 to 8. If no. of people is lower, the no of days taken to do the work will be more. So 20 (the initial no. of days) is multiplied by 10/8, a number greater than 1, to increase the number of days. From where do we get (3/1)? Amount of work increases from 1/4 to 3/4. If more work has to be done, no. of days required will be more. So we further multiply by (3/4)/(1/4) i.e. 3/1, a number greater than 1 to further increase the number of days. This gives us the expression \(20*(\frac{10}{8})*(\frac{3}{1})\) We get that the work will be complete in another 75 days. Answer (C)
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 26 Feb 2015
Posts: 5

Re: A contractor undertakes to do a job within 100 days and hires 10 peopl
[#permalink]
Show Tags
12 Feb 2016, 18:58
We can also use the concept of mandays here
100 days >10men so the job includes 100*10=1000 mandays
After 20 days
1/4 of Job is completed so 1/4 X 1000 mandays=250 mandays Job is done
Now the Balance Job=1000250=750 mandays worth of Job Since 2 men are fired so B/L men=8
Therefore Total no. of days of Job=750 manday/8 days = 375/4=94 days (approx.)
Now since this is total and Ques. is asking for additional no. of days, So 9420=74 days The nearest approx. to answer is 75
Ans: C (75 days)



Math Expert
Joined: 02 Aug 2009
Posts: 7046

Re: A contractor undertakes to do a job within 100 days and hires 10 peopl
[#permalink]
Show Tags
12 Feb 2016, 19:16
Bunuel wrote: A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?
(A) 60 (B) 70 (C) 75 (D) 80 (E) 100
Kudos for a correct solution. Hi, Just a POINT on wordings.. It would have been better, if it mentioned that all worked with same and constant speedA quick approach could be.. so we assume that all have same capabilities to work.. 1/4 work done in 20 days.. so remaining work can be done in 60 days with 10 person.. in the same ratio, the work can be done by 1 person in 60*10 days=600.. and 8 will do it in= 600/8= 75 daysC
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Intern
Joined: 14 Dec 2014
Posts: 19
Concentration: Technology

Re: A contractor undertakes to do a job within 100 days and hires 10 peopl
[#permalink]
Show Tags
13 Feb 2016, 06:27
Rate = Work/ Time
10 person team: Work = 1/4 total Time = 20 days Rate = (1/4)/ 20 days = 1/4 *1/20 = 1/80
Rate of 1 person > 1/80 * 1/10 = 1/800
8 person team: Work = 3/4 total Rate = 1/ 800 * 8 = 1/100 Time = (3/4) / (1/100) = 3/4 *100 = 75 days



Intern
Joined: 07 Jan 2017
Posts: 19
Location: India
Concentration: Other, Other
WE: Medicine and Health (Pharmaceuticals and Biotech)

Re: A contractor undertakes to do a job within 100 days and hires 10 peopl
[#permalink]
Show Tags
08 Jul 2017, 08:29
Estimated rate by contractor is 1/1000 (10 workers *100 days) As per this rate,the amount of work completed after 20 days should have been 20% which is not the case as 25 % work was done after 20 days by 10 workers Thus the actual rate of workers would be 1/x*10*20=1/4————1/x=1/800 At the rate of 1/800, 8 workers would require 'y' days to complete the rest of the 75% work 1/800*8*y=3/4 y=3/4*800/8 y=75



Manager
Joined: 24 Jun 2017
Posts: 122

Re: A contractor undertakes to do a job within 100 days and hires 10 peopl
[#permalink]
Show Tags
14 Aug 2017, 08:52
My solution Let’s assume that each of the men’s performance is 1 piece of work Then (1*10) * 100 = 1000 should be produced in 100 days by 10 men during 20 days they did a quarter of required 1000 so it’s 250 (1.25 * 10) *20 = 250 He fires 8 and the remaining work is 750 Then (1.25*8)*x=750 solve for x = 75



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830

Re: A contractor undertakes to do a job within 100 days and hires 10 peopl
[#permalink]
Show Tags
18 Aug 2017, 07:58
Bunuel wrote: A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?
(A) 60 (B) 70 (C) 75 (D) 80 (E) 100 The rate of 10 people is (1/4)/20 = 1/80. After firing 2 people, 8 people are left. We can use the following proportion to determine the rate of 8 people: 10/(1/80) = 8/x 800 = 8/x 800x = 8 x = 1/100 Thus, it will take (3/4)/(1/100) = 300/4 = 75 days more to complete the job. Answer: C
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 21 Sep 2016
Posts: 29

Re: A contractor undertakes to do a job within 100 days and hires 10 peopl
[#permalink]
Show Tags
18 Sep 2017, 22:21
In 20 days, 10 employees have done 1/4 of the entire job.
That means the daily rate of 1 employee is: 1/(40*20) = 1/800
Now it is stated that 2 were fired, which leaves us with 8 guys to the 3/4 of the initial job and we want to know in how many days they'll be able to do it. Let "x" be that number of days:
\((1/800) * 8x = 3/4\)
\(x = (3*100)/4\) \(= 75 days.\)



Intern
Joined: 16 Jul 2016
Posts: 20

Re: A contractor undertakes to do a job within 100 days and hires 10 peopl
[#permalink]
Show Tags
25 Sep 2017, 01:04
let the total amount of work to be done be X Then, 20*10=1/4X X=800 and 25% of the work is done in 20 days which means 200 unit of work is completed by 10 men in 20 days and the rest 600 unit of work is to be done by 8 men Therefore,600/8= 75
Kudos if you find this explanation helpful



Manager
Joined: 30 Apr 2017
Posts: 64

Re: A contractor undertakes to do a job within 100 days and hires 10 peopl
[#permalink]
Show Tags
21 Oct 2017, 09:37
GMATinsight wrote: Bunuel wrote: A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?
(A) 60 (B) 70 (C) 75 (D) 80 (E) 100
Kudos for a correct solution. CONCEPT: \(\frac{(Machine_Power * Time)}{Work} = Constant\)i.e. \(\frac{(M_1 * T_1)}{W_1} = \frac{(M_2 * T_2)}{W_2}\) In 10 workers finish 1/4 work in 20 days Remaining work = 1(1/4) = 3/4 No. of People left to work = 10(total)  2(fired) = 8 Days left = ? \(\frac{(10 * 20)}{(1/4)} = \frac{(8 * T_2)}{(3/4)}\) i.e. \(T_2 = 75\) Days Answer: option C Hi could you explain the concept, please? unfortunately, I haven't seen it yet



PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82

Re: A contractor undertakes to do a job within 100 days and hires 10 peopl
[#permalink]
Show Tags
21 Oct 2017, 09:48
soodia wrote: GMATinsight wrote: Bunuel wrote: A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?
(A) 60 (B) 70 (C) 75 (D) 80 (E) 100
Kudos for a correct solution. CONCEPT: \(\frac{(Machine_Power * Time)}{Work} = Constant\)i.e. \(\frac{(M_1 * T_1)}{W_1} = \frac{(M_2 * T_2)}{W_2}\) In 10 workers finish 1/4 work in 20 days Remaining work = 1(1/4) = 3/4 No. of People left to work = 10(total)  2(fired) = 8 Days left = ? \(\frac{(10 * 20)}{(1/4)} = \frac{(8 * T_2)}{(3/4)}\) i.e. \(T_2 = 75\) Days Answer: option C Hi could you explain the concept, please? unfortunately, I haven't seen it yet Hi soodia, the formula can be derived by applying unitary method \(10\) people completed \(\frac{1}{4}\)th work in \(20\) days so \(1\) people will complete whole i.e \(1\) work in \(20*10*4\) (no of days will increase as only \(1\) person is working) Hence \(8\) people will complete the remaining \(\frac{3}{4}\)th work in \(\frac{20*10*4*3}{8*4} = 75\) days



Manager
Joined: 22 Nov 2016
Posts: 213
Location: United States
Concentration: Leadership, Strategy
GPA: 3.4

Re: A contractor undertakes to do a job within 100 days and hires 10 peopl
[#permalink]
Show Tags
10 Nov 2017, 13:11
lenric wrote: In 20 days, 10 employees have done 1/4 of the entire job.
That means the daily rate of 1 employee is: 1/(40*20) = 1/800
Now it is stated that 2 were fired, which leaves us with 8 guys to the 3/4 of the initial job and we want to know in how many days they'll be able to do it. Let "x" be that number of days:
\((1/800) * 8x = 3/4\)
\(x = (3*100)/4\) \(= 75 days.\) By far the quickest method. Nice one.
_________________
Kudosity killed the cat but your kudos can save it.



Manager
Joined: 02 Aug 2017
Posts: 66
Concentration: Strategy, Nonprofit
GPA: 3.71

Re: A contractor undertakes to do a job within 100 days and hires 10 peopl
[#permalink]
Show Tags
24 Aug 2018, 21:14
The approach below is detailed for the understanding purposes, however once you know the logic behind it, you'd be able to solve the question faster. Consider giving Kudos if it helps :D Posted from my mobile device
Attachments
15351740000946689347440359215639.jpg [ 2.07 MiB  Viewed 2002 times ]
_________________
Everything is in flux, nothing stays still
MGMAT1 :590 Q42 V30 (07/07/18) VERITAS :660 Q48 V33 (16/07/18) GMATPREP1 :690 Q46 V36 (22/07/18) GMATPREP2 :740 Q51 V39 (06/08/18) ECONOMIST :740 Q49 V44 (11/08/18) KAPLAN :690 Q49 V36 (17/08/18) PRINCETON :690 Q48 V38 (26/08/18) MGMAT2 :720 Q43 V45 (02/09/18)




Re: A contractor undertakes to do a job within 100 days and hires 10 peopl &nbs
[#permalink]
24 Aug 2018, 21:14



Go to page
1 2
Next
[ 23 posts ]



