Twenty-four men can complete a work in sixteen days.

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hazelnut01: Master | Next Rank: 500 Posts; Posts: 157; Joined: Sat Nov 19, 2016 5:34 amFollowed by: 4 members; Thanked: 2 times

by hazelnut01 » Thu Mar 16, 2017 10:27 pm

Twenty-four men can complete a work in sixteen days.Thirty-two women can complete the same work in twenty-four days. Sixteen men and sixteen women started working for twelve days.How many more men are to be added to complete the work remaining work in 2 days?

A .16
B. 24
C. 36
D. 48
E. 54

Source : Veritas Prep
Official answer = B

Last edited by hazelnut01 on Tue May 16, 2017 3:33 am, edited 3 times in total.

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Source: Beat The GMAT — Problem Solving | Thu Mar 16, 2017 10:27 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Thu Mar 16, 2017 10:32 pm

ziyuenlau wrote:Twenty-four men can complete a work in sixteen days.Thirty-two women can complete the same work in twenty-four days. Sixteen men and sixteen women started working for twelve days.How many more men are to be added to complete the work remaining work in 2 days?

A .16
B. 24
C. 36
D. 48
E. 54

Hi ziyuenlau,

Always post a question with an official answer and if you know the source, pl put that also.

-Jay
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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Thu Mar 16, 2017 11:50 pm

ziyuenlau wrote:Twenty-four men can complete a work in sixteen days.Thirty-two women can complete the same work in twenty-four days. Sixteen men and sixteen women started working for twelve days.How many more men are to be added to complete the work remaining work in 2 days?

A .16
B. 24
C. 36
D. 48
E. 54

Official answer = B

Hi ziyuenlau,

We have the following.

24 Men take 16 days for a work
32 Women take 24 days for the same work

16 Men and 16 women work for 12 days.

Let's calculate the part of work completed in 12 days.

Since 24 Men take 16 days for a work, 16 Men would take 16*24/16 = 24 days for the work

Since 32 women take 24 days for the same work, 16 women would take 48 days for the same work

Total work done by 16 Men and 16 women work in 12 days = 12/24 + 12/48 = 1/2 + 1/4 = 3/4 part of the work.

Thus, 1 - 3/4 = 1/4 part of the work is remaining

For the next 2 days, 16 Men and 16 women work who are already working on the project plus a few men also work.

Let's calculate the part of the remaing work done by the exisiting team of 16 men and 16 women

Work done by 16 men and 16 women in 2 days = 2/24 + 2/48 = 1/12 + 1/24 = 1/8 part of the work.

Thus, the part of the work remaining for the extra men to be done in 2 days = 1/4 - 1/8 = 1/8 part of the work.

Since 24 men take 16 days to complete the work, 24*16/2 men take 2 days to complete the full work.

Or, (24*16/2)*1/8 = 24 men take 2 days to complete the 1/8 part of the work.

Additional needed = 24.

The correct answer: B

Hope this helps!

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by [email protected] » Fri Mar 17, 2017 1:44 pm

Hi ziyuenlau,

Before we get into this question, you've been posting a variety of 'tougher' prompts lately - so unless you're already scoring above 700 in your practice Exams (or on the Official GMAT), then you might be focusing on the wrong things.

In these types of 'rate' questions, it often helps to think in terms of the TOTAL work that must be done to complete the task. If a 24-man crew can complete the job in 16 days, then that means that (24)(16) = 384 man-days of effort are required to complete the job. If a 32-woman crew can complete the job in 24 days, then that means that (32)(24) = 768 woman-days of effort are required to complete the job.

Before we do anything else, it's important to compare these numbers: 384 and 768. Since 384 is exactly HALF of 768, in this question that means that the work that a woman does in 1 day = 1/2 of the work that a man does in 1 day.

We're told that 16 men and 16 women work for 12 days each. That means they complete....

(16 men)(12 days) = 192 man-days of work = 1/2 of the job gets done
(16 women)(12 days) 192 woman-days of work = 1/4 of the job gets done

1/2 + 1/4 = 3/4... so after 12 days, 3/4 of the job is done - and 1/4 of the job remains

We're going to add a certain number of men, so that the job is completed in 2 more days. First though, we have to figure out how much more of the job gets completed with the existing people during that time...

(16 men)(2 days) = 32 man-days of work = 1/12 of the job gets done
(16 women)(2 days) 32 woman-days of work = 1/24 of the job gets done

During the next 2 days, the existing people will complete 1/12 + 1/24 = 3/24 of the job gets done

That leaves us with 1/4 - 3/24 = 3/24 of the job remains. 3/24 of 384 man-days = 48 man-days of work. The extra men that will be added will work for 2 days each, so....

(X men)(2 days each) = 48 days of man-work
X = 24

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Mar 17, 2017 2:30 pm

ziyuenlau wrote:Twenty-four men can complete a work in sixteen days.Thirty-two women can complete the same work in twenty-four days. Sixteen men and sixteen women started working for twelve days.How many more men are to be added to complete the work remaining work in 2 days?

A .16
B. 24
C. 36
D. 48
E. 54

Let the rate for each man = 1 widget per day, implying that the rate for 24 men = 24 widgets per day.
Since 24 men complete the job in 16 days, the total amount of work = rt = 24*16 widgets.

Since 32 women require 24 days, the rate for 32 women = w/t = (24*16)/24 = 16 widgets per day.
Since 32 women produce 16 widgets per day, the rate for each woman = (daily output)/(number of women) = 16/32 = 1/2 widget per day.
Thus, the combined rate for 16 men and 16 women = (16*1) + (16 * 1/2) = 24 widgets per day.

In 12 days, the amount of work produced by 16 men and 16 women = rt = 24*12 widgets.
Remaining work = (total work) - (work produced in the first 12 days) = (24*16) - (24*12) = 24(16-12) = 24*4 = 96 widgets.

To complete the remaining work in 2 days, the required rate = (remaining work)/(number of days) = 96/2 = 48 widgets per day.
Since the rate must increase from the value in red to the value in blue -- an increase of 24 widgets per day -- 24 more men are required.

The correct answer is B.

What is the source of this problem?
It seems sexist to make the rate for each man twice that for each woman.
Official problems strive to avoid this sort of bias.

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Mo2men: Legendary Member; Posts: 712; Joined: Fri Sep 25, 2015 4:39 amFollowed by: 5 members; Thanked: 14 times

by Mo2men » Sat Mar 18, 2017 9:42 am

GMATGuruNY wrote:
ziyuenlau wrote:Twenty-four men can complete a work in sixteen days.Thirty-two women can complete the same work in twenty-four days. Sixteen men and sixteen women started working for twelve days.How many more men are to be added to complete the work remaining work in 2 days?

A .16
B. 24
C. 36
D. 48
E. 54
Let the rate for each man = 1 widget per day, implying that the rate for 24 men = 24 widgets per day.
Since 24 men complete the job in 16 days, the total amount of work = rt = 24*16 widgets.

Since 32 women require 24 days, the rate for 32 women = w/t = (24*16)/24 = 16 widgets per day.
Since 32 women produce 16 widgets per day, the rate for each woman = (daily output)/(number of women) = 16/32 = 1/2 widget per day.
Thus, the combined rate for 16 men and 16 women = (16*1) + (16 * 1/2) = 24 widgets per day.

In 12 days, the amount of work produced by 16 men and 16 women = rt = 24*12 widgets.
Remaining work = (total work) - (work produced in the first 12 days) = (24*16) - (24*12) = 24(16-12) = 24*4 = 96 widgets.

To complete the remaining work in 2 days, the required rate = (remaining work)/(number of days) = 96/2 = 48 widgets per day.
Since the rate must increase from the value in red to the value in blue -- an increase of 24 widgets per day -- 24 more men are required.

The correct answer is B.

What is the source of this problem?
It seems sexist to make the rate for each man twice that for each woman.
Official problems strive to avoid this sort of bias.

Dear Mitch,

This question is aptitude question from R.S AGGARWAL.

Why is it sort of bias?Can't we establish relationships between men and women rates.

Thanks

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by GMATGuruNY » Sat Mar 18, 2017 12:58 pm

Mo2men wrote:
GMATGuruNY wrote: What is the source of this problem?
It seems sexist to make the rate for each man twice that for each woman.
Official problems strive to avoid this sort of bias.
Dear Mitch,

This question is aptitude question from R.S AGGARWAL.

Why is it sort of bias?Can't we establish relationships between men and women rates.

Thanks

To many people, a faster worker = a BETTER worker.
As a result, the problem above seems to imply that men make better workers than women, since the men in the problem work twice as fast as the women.
Implying that one gender is somehow better than the other seems sexist.
This sort of bias can be avoided as follows:
Twenty-four machines of Type A can complete a job in sixteen days. Thirty-two machines of Type B can complete the same job in twenty-four days.

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by ceilidh.erickson » Wed Mar 22, 2017 10:05 am

It's interesting to note that the GRE Official Guide, 3rd Edition that came out a few months ago recently changed all questions that address gender to be gender-neutral. For example, a question that previous read "the ratio of boys to girls in a certain class..." would be changed to "the ratio of juniors to seniors..." and "the percentage of female employees" to "the percentage of full-time v. part-time employees," etc.

GMAT problems, as Mitch points out, take pains not to suggest that women or racial minorities make less money, are less represented as employees, work at slower rates, etc. I would predict that they'll soon follow the GRE's example and get rid of questions that address gender altogether!

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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by Scott@TargetTestPrep » Thu Mar 23, 2017 3:20 pm

ziyuenlau wrote:Twenty-four men can complete a work in sixteen days.Thirty-two women can complete the same work in twenty-four days. Sixteen men and sixteen women started working for twelve days.How many more men are to be added to complete the work remaining work in 2 days?

A .16
B. 24
C. 36
D. 48
E. 54

Since 24 men can complete a work in 16 days, the rate of 24 men is 1/16, and hence the rate of 1 man is (1/16)/24 = 1/384. Similarly, 32 women can complete the same work in 24 days, the rate of 32 women is 1/24, and hence the rate of 1 woman is (1/24)/32 = 1/768. Thus, the rate for 16 men and 16 women is 16 x (1/384) + 16 x (1/768) = 1/24 + 1/48 = 2/48 + 1/48 = 3/48 = 1/16.

Since these 16 men and 16 women worked for 12 days, they completed (1/16) x 12 = 12/16 = 3/4 of the job.

Thus, 1/4 of the job is left to be done. To find the number of additional men needed to complete the remaining work in 2 days, we can let n = the additional men needed and create the following equation (keep in mind that the rate of each man is 1/384 and the rate of the existing 16 men and 16 women is 1/16):

n(1/384)(2) + (1/16)(2) = 1/4

n/192 + 1/8 = 1/4

n/192 = 1/8

8n = 192

n = 24

Answer: B

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