Find all School-related info fast with the new School-Specific MBA Forum

It is currently 22 Oct 2014, 15:19

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If 20 men or 24 women or 40 boys can do a job in 12 days

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 10 Nov 2004
Posts: 44
Followers: 1

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

If 20 men or 24 women or 40 boys can do a job in 12 days [#permalink] New post 01 Dec 2004, 10:50
If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys take to do a job four times as big working for 5 hours a day for 12 days? (1) 8 men (2) 12 men (3) 2 men (4) 24 men
Manager
Manager
User avatar
Joined: 31 Aug 2004
Posts: 169
Location: Vancouver, BC, Canada
Followers: 1

Kudos [?]: 4 [0], given: 0

Re: job problem [#permalink] New post 01 Dec 2004, 18:52
revital wrote:
If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys take to do a job four times as big working for 5 hours a day for 12 days? (1) 8 men (2) 12 men (3) 2 men (4) 24 men


Mmm...a tough one. I can only come up the following though, need someone else to show me the light!

Let x, y, z be the portion of a job a man, a woman and a boy does. Let k be the number of man required for the second job.

20/x + 24/y + 40/z = 1

My logic is (# of man) * the potion of the job a man can do + (# of woman) * the potion of the job a woman can do + (# of boy) * the potion of the job a boy can do

Same idea apply to the second job

k/x + 6/y + 2/z = 1

Now I am stuck here. I do not know how to incorporate the days and hours into the equation.

Need help!!!

:???
Director
Director
User avatar
Joined: 16 Jun 2004
Posts: 893
Followers: 1

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

 [#permalink] New post 01 Dec 2004, 21:36
I think the answer choices may be wrong...Here's my logic

a) looking at the ratios, we get that 2 boys is equal to 1 men (interms of the rate at which they work)
b) 6 Women by the same above logic equals only 5 men working
c) now, the question is 6W + 2B + XMen to complete a job 4 times as big and at lesser no. of hours per day.
d) that is equivalent of saying 6M (2B + 6 women = 6Men) + X Men.
e) 20 Men take 96 manhours (12days *8hrs/day) to doing that job. So, 4 times that job would take 80 men.
f) We already have 6M equivalent work contributed by 2boys and 6 women. So, it will take remaining 74 men (80-6) to doing 4 times the job @8hrs /day.
g) So, if the number of hrs/day is going to be be only 3 hrs, then the no. fo days will increase by 8/5 times (8/5 is derive from 96/60).

In a nutshell, the it will be surely more than the 24 men mention in the answer choice.

I am unsure, if I am missing anything. Anyone?
Director
Director
User avatar
Joined: 16 Jun 2004
Posts: 893
Followers: 1

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

 [#permalink] New post 01 Dec 2004, 22:29
Ok I think I am right in my earlier approach which was completely intuitive. However, I luckily read one more interesting method that works well too...

Important to note this: More work, More men needed; Fewer Hours, More Men needed;Fewer days, More Men needed.

ok, lets draw something for easy working

Men Days hours Job
20 12 8 1
x 12 5 4

x= 20*(12/12)*(8/5)*(4/1) = 128 M

As said earlier in my other post...6W and 2Boys equal 6men. So, we need 128-6= 122 men.
Manager
Manager
avatar
Joined: 15 Jul 2004
Posts: 75
Location: London
Followers: 1

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

job problem [#permalink] New post 02 Dec 2004, 03:40
I get 113 men

My reasoning:

1 job takes 20 men 12days at 8 h per day = 1 job takes 20 men 96 h. Therefore the fraction of job done by 1 man in 1 hour is 1 / (20 * 96) (units are job / (man *h)).

Following the same reasoning:
1/(24*96) (jobs / woman*h))
1/(40*96) (jobs / boy*h))

We now know the fraction of job per type of person in 1 h.

The new job will be 4 (original) jobs in 12 * 5 = 60 hours

I used the following equation:

Job/ h = fraction of job per hour done by 2 boys + fraction of job per hour done by 6 women + fraction of job per hour done by X men

4/60 (jobs / h) = [1/(40*96) (jobs / boy*h)) * 2 boys] + [1/(24*96) (jobs / woman*h)) * 6 women] + [1/(20*96) (jobs / man*h)) * X men]

If I didn’t make any mistake in the calculations: X=113 men
Manager
Manager
avatar
Joined: 15 Jul 2004
Posts: 75
Location: London
Followers: 1

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

job problem [#permalink] New post 02 Dec 2004, 05:38
Revital,

can you explain why it is C, please?
Manager
Manager
User avatar
Joined: 07 Nov 2004
Posts: 89
Location: London
Followers: 1

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

 [#permalink] New post 02 Dec 2004, 06:13
ans = 2 men. Took me a while though (>10 mins)

It takes 96 hours for 20 men or 24 women or 20 boys to complete the first job. This means that as far a productivity goes, 1 man = 6/5 women = 2 boys. [1.1]

We have to think in terms of man-hours here.
The number of man-hours required of 1 man to complete the first job = 4 * the number of hour required of one man to complete the new job

hence we have,

20men * 96hours = number of men required * 60 hours * 4
It yields
number of men required = 8
But there are 6 women and 2 boys working on the job. Using 1.1 we can say that, 6 men (6 women = 5 men and 2 boys = 1 man) working on the new job is equivalent to 6 women and 2 boys working on the job.

Hence we need 2 extra blokes to help 6 women and 2 boys out.
Director
Director
User avatar
Joined: 16 Jun 2004
Posts: 893
Followers: 1

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

 [#permalink] New post 02 Dec 2004, 07:44
oxon wrote:
20men * 96hours = number of men required * 60 hours * 4


Oxon,
Sorry I dont understand this part.

Even if we take manhours, if 20 Men can complete a job in 96 hours, It needs 80 men to complete a job that is 4 times bigger. Am I getting caught with only one view? Pls advise.

Surprisingly, If the question were to read '4 times smaller in size of the original job' then the answer is 2.

The 'x' in my previous post would be = 20*(12/12)*(8/5)*(1/4) = 8 Men.
2 boys and 6 women = 6 Men. SO, total men needed is 8-6 = 2.
Manager
Manager
User avatar
Joined: 07 Nov 2004
Posts: 89
Location: London
Followers: 1

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

 [#permalink] New post 02 Dec 2004, 09:24
venksune,

In my first attempt I got 122 men. Then, I noticed the following:
- The new job if 4 times as big as the first one. How could one the number of adult male workers required be less than 20 given that?
a. they reduced the number of women and boys workers.
b. All have less time to complete the task 60 hours vs. 96 hours.

Surely the new job is 4 times as small as the first one. This is why I stated in my post the following:
The number of man-hours required to complete the first job = 4 * the number of hour required to complete the new job
hence,
20 * 8 * 12 = number of man hours to complete the new job (adult male workers only) * 5 * 12 * 4

so yeah, basically there is typo in the question stem and 122 men is the correct answer to the question.
Director
Director
User avatar
Joined: 25 Jan 2004
Posts: 728
Location: Milwaukee
Followers: 2

Kudos [?]: 10 [0], given: 0

 [#permalink] New post 02 Dec 2004, 11:06
Here is a another way ( Easy now after banging my head for some time )


First establish a relative work ratio

6 women 60 hour can do 6 * 60/96 *24 =5/32 of work
2 boys in 60 hour can do 2* 60/96*40 =1/32 of work

now X men would have to do 4-6/32 = 61/16 work in 60 hours

further
we know X *60/96*24 can do 61/16 work in 60 hours hence

61/16 = X * 60/96*20

we get X = 122
_________________

Praveen

  [#permalink] 02 Dec 2004, 11:06
    Similar topics Author Replies Last post
Similar
Topics:
14 Experts publish their posts in the topic If w women can do a job in d days, then how many days will mendelay 16 10 Sep 2009, 06:18
Experts publish their posts in the topic If w women can do a job in d days, then how many days will puma 4 12 Apr 2008, 11:10
13 men and 7 boys can finish a job in 7 days, while 6 boys nfa1rhp 4 22 Jul 2007, 12:08
13 men and 7 boys can finish a job in 7 days, while 6 boys krisrini 5 05 Jan 2006, 03:23
If 15 men or 24 women or 35 boys do a piece of work in 12 anirban16 4 19 Mar 2005, 09:21
Display posts from previous: Sort by

If 20 men or 24 women or 40 boys can do a job in 12 days

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.