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# Twenty-four men can complete a work in sixteen days.Thirty-two women c

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Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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16 Mar 2017, 12:10
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Question Stats:

48% (03:19) correct 52% (03:29) wrong based on 321 sessions

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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
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Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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16 Mar 2017, 21:10
20
1
8
Chemerical71 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

First find the relation of rate of work done by men vs women.

24 men complete the work in 16 days.
32 women can complete the same work in 24 days.
So 24 women will take 24 * (32/24) = 32 days to complete the work

Same number of women take twice the time (16 days vs 32 days) so their rate of work is half.
So 16 women are equivalent to 8 men work-wise.

So 16 + 8 = 24 men start working and work for 12 days. They complete the work in 16 days so they need another 4 days to complete. But if we want them to complete the work in half the time (2 days), we will need twice the work force. So we need another 24 men.

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Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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16 Mar 2017, 20:49
3
5
24 men ----------- 16 days ------------ 1 complete work
1 man ------------ 1 day ------------1/(24*16) portion work

32 women ----------- 24 days ------------ 1 complete work
1 woman ------------ 1 day ------------1/(32*24) portion work

Hence,
1 man &1 woman ------------ 1 day ------------{1/(32*24) + 1/(24*16)} portion work = 1(/24)*(1/16 + 1/32) = (1/24)*(3/32) = (1/8)*(1/32)
Now,
16 man & 16 woman ------------ 1 day ------------ 16* (1/8)*(1/32) portion work = 2*(1/32) = 1/16
16 man & 16 woman ------------ 12 day ------------ 12*(1/16) = 3/4
Remaining work - 1/4

Now, extra work in next 2 days: 1/4 - 2*(1/16) = 1/8
Then, extra men required in next 2 days: (24*16)/(2*8) = 24 .

This is not a SUB-600 level question.
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Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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16 Mar 2017, 20:54
saswata4s wrote:
24 men ----------- 16 days ------------ 1 complete work
1 man ------------ 1 day ------------1/(24*16) portion work

32 women ----------- 24 days ------------ 1 complete work
1 woman ------------ 1 day ------------1/(32*24) portion work

Hence,
1 man &1 woman ------------ 1 day ------------{1/(32*24) + 1/(24*16)} portion work = 1(/24)*(1/16 + 1/32) = (1/24)*(3/32) = (1/8)*(1/32)
Now,
16 man & 16 woman ------------ 1 day ------------ 16* (1/8)*(1/32) portion work = 2*(1/32) = 1/16
16 man & 16 woman ------------ 12 day ------------ 12*(1/16) = 3/4
Remaining work - 1/4

Now, extra work in next 2 days: 1/4 - 2*(1/16) = 1/8
Then, extra men required in next 2 days: (24*16)/(2*8) = 24 .

This is not a SUB-600 level question.
Then, extra men required in next 2 days: (24*16)/(2*8) = 24 . please explain this step again.
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Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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16 Mar 2017, 23:09
VeritasPrepKarishma wrote:
Chemerical71 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

First find the relation of rate of work done by men vs women.

24 men complete the work in 16 days.
32 women can complete the same work in 24 days.
So 24 women will take 24 * (32/24) = 32 days to complete the work

Same number of women take twice the time (16 days vs 32 days) so their rate of work is half.
So 16 women are equivalent to 8 men work-wise.

So 16 + 8 = 24 men start working and work for 12 days. They complete the work in 16 days so they need another 4 days to complete. But if we want them to complete the work in half the time (2 days), we will need twice the work force. So we need another 24 men.

Dear VeritasPrepKarishma, Does the font highlighted in red reflecting the relationship is inversely proportional instead of directly proportional?

For example, 10 apples cost $20, 5 apples will cost (5*$20/10=$10). _________________ "Be challenged at EVERY MOMENT." “Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.” "Each stage of the journey is crucial to attaining new heights of knowledge." Rules for posting in verbal forum | Please DO NOT post short answer in your post! Advanced Search : https://gmatclub.com/forum/advanced-search/ Director Status: Come! Fall in Love with Learning! Joined: 05 Jan 2017 Posts: 535 Location: India Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c [#permalink] ### Show Tags 17 Mar 2017, 00:52 5 2 Chemerical71 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 work be z rate of doing work for man and woman be x and y respectively According to question 24*16*x = z 32*24*y = z therefore 24*16*x = 32*24*y or x = 2y work done in 12 days = (16x +16y)12 = (32y + 16y) 12 = 48*12y = 24*24y work left = 32*24y-24*24y = 8*24y work left = (no of men added rate+ current workers rate)*2 or 8*24y = (N*x +16x+16y)*2 putting x = 2y 4*24y = 2Ny+48y 2Ny = 48y or N = 24. Option B _________________ GMAT Mentors Retired Moderator Joined: 04 Aug 2016 Posts: 479 Location: India Concentration: Leadership, Strategy GPA: 4 WE: Engineering (Telecommunications) Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c [#permalink] ### Show Tags 17 Mar 2017, 02:42 ziyuen wrote: VeritasPrepKarishma wrote: Chemerical71 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 First find the relation of rate of work done by men vs women. 24 men complete the work in 16 days. 32 women can complete the same work in 24 days. So 24 women will take 24 * (32/24) = 32 days to complete the work Same number of women take twice the time (16 days vs 32 days) so their rate of work is half. So 16 women are equivalent to 8 men work-wise. So 16 + 8 = 24 men start working and work for 12 days. They complete the work in 16 days so they need another 4 days to complete. But if we want them to complete the work in half the time (2 days), we will need twice the work force. So we need another 24 men. Answer (B) Dear VeritasPrepKarishma, Does the font highlighted in red reflecting the relationship is inversely proportional instead of directly proportional? For example, 10 apples cost$20, 5 apples will cost (5*$20/10=$10).

Total Work completed = Rate of work of each man * total # of man * total time

Rate of work of each man = Total Work completed / (total # of man * total time) = 1/ (24*16)
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Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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18 Mar 2017, 11:58
2
1
ziyuen wrote:
VeritasPrepKarishma wrote:
Chemerical71 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

First find the relation of rate of work done by men vs women.

24 men complete the work in 16 days.
32 women can complete the same work in 24 days.
So 24 women will take 24 * (32/24) = 32 days to complete the work

Same number of women take twice the time (16 days vs 32 days) so their rate of work is half.
So 16 women are equivalent to 8 men work-wise.

So 16 + 8 = 24 men start working and work for 12 days. They complete the work in 16 days so they need another 4 days to complete. But if we want them to complete the work in half the time (2 days), we will need twice the work force. So we need another 24 men.

Dear VeritasPrepKarishma, Does the font highlighted in red reflecting the relationship is inversely proportional instead of directly proportional?

For example, 10 apples cost $20, 5 apples will cost (5*$20/10=\$10).

The relation between no. of workers and no of days is inversely proportional.
If there are fewer women, no of days taken will be more.

No of women * No of days = Constant

32 women * 24 days = 24 women * ?? days

?? days = 24 days * (32 women/24 women)

?? days = 24 days

For more on direct and inverse proportion, check:
https://www.veritasprep.com/blog/2013/0 ... -directly/
https://www.veritasprep.com/blog/2013/0 ... inversely/
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Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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21 Mar 2017, 06:20
7
4
Chemerical71 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

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Re: Twenty-four men can complete a job in sixteen days. Thirty-two women  [#permalink]

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15 May 2017, 11:28
2
1
Bunuel wrote:
Twenty-four men can complete a job in sixteen days. Thirty-two women can complete the same job in twenty-four days. Sixteen men and sixteen women started working on the job for twelve days. How many more men must be added to complete the job in 2 days?

(A) 16

(B) 24

(C) 36

(D) 48

(E) 54

1M 1D work=1/(16*24)
1W 1D work=1/(24*32)

16M 1D work=1/24=2/48
16W 1D work=1/48

16M&W 1D work=3/48=1/16
16M&W 12D work=12/16

Hence remaining work=4/16=1/4 -------> this work should be completed by the additional men

1M 1D work=1/(16*24)
1M 2D work=1/(16*12)
xM 2D work=x/(16*12), this must be equal to 1/4

x/(16*12)=1/4
=> x=48

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Re: Twenty-four men can complete a job in sixteen days. Thirty-two women  [#permalink]

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15 May 2017, 11:46
1
Lets take lcm of 16,24 and 32 i.e 96. So let the work job be 96.
Now for men let their one day effort be x. So x*24*16= 96, hence x= 1/4
Similary for women let their one day effort per person be y . So y*32*24=96
Y= 1/8.
Now (1/4+1/8)*16*12=72. So 24 units of work is left. Now let no of men be z 1/4*2*z= 24.
Hence z =48

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Twenty-four men can complete a job in sixteen days. Thirty-two women  [#permalink]

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15 May 2017, 12:18
This one took a while to do simply bc of all the calculations (if there is a quick way please let me know)

I ended up with 48, D.

Men rate = 1/384
Women rate = 1/768

Combined and through 14 days = 336/384, 48 being the difference

Edit: upon further review, I made a mistake and didn't account for the two days. It should be 24 additional men, making the total 48 on day 12. This would produce the additional 96 units needed
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Twenty-four men can complete a job in sixteen days. Thirty-two women  [#permalink]

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15 May 2017, 16:55
1
Excellent question.
700 level for sure ..
Here is what I did on this question---->

Let us decode the statements ==>
Let the complete work be designated by W.

Twenty-four men can complete a job in sixteen day.
Speed of each men => W/(16*24) per day

Thirty-two women can complete the same job in twenty-four days.
Speed of each women => W/(32*24) per day

16 men and 16 women stated working

Combined speed of 16 men and 16 women => W/(16*24) * 16 + W/(32*24) *16 => W/24+W/48 => W/16 per day
Now combining they work for 12 Days =>

Work done => 12*W/16 => 3W/4
Left over work => W-3W/4 => W/4

Now let more men =x

Hence-->
2* [(x+16) W/(16*24) + 16*W/(32*24)] = W/4

Solving this we get => x=24

Hence B.

SMASH THAT B.

Looking forward to the OE.

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Twenty-four men can complete a job in sixteen days. Thirty-two women  [#permalink]

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16 May 2017, 00:53
3
gmatexam439 wrote:
Bunuel wrote:
Twenty-four men can complete a job in sixteen days. Thirty-two women can complete the same job in twenty-four days. Sixteen men and sixteen women started working on the job for twelve days. How many more men must be added to complete the job in 2 days?

(A) 16

(B) 24

(C) 36

(D) 48

(E) 54

1M 1D work=1/(16*24)
1W 1D work=1/(24*32)

16M 1D work=1/24=2/48
16W 1D work=1/48

16M&W 1D work=3/48=1/16
16M&W 12D work=12/16

Hence remaining work=4/16=1/4 -------> this work should be completed by the additional men

1M 1D work=1/(16*24)
1M 2D work=1/(16*12)
xM 2D work=x/(16*12), this must be equal to 1/4

x/(16*12)=1/4
=> x=48

You did all the hard work.
But missed out just at the very end.

The highlighted portion is incorrect.

Here is the corrected version -->

The work 1/4 would be done by both x men and 16 women.
You forgot to take 16 women into account.
NOTE -> You have taken the entire men's number as x.

So work done by x men and 16 women in 2 days => 2[x/24*16 +16/24*32] =1/4
x=40
Hence additional men required => 40-16 => 24

Smash that B.

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Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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16 May 2017, 09:05
1
1
Chemerical71 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

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

So, Total mandays = 24*16 => 384

Quote:
Thirty-two women can complete the same work in twenty-four days.

So, Total womandays = 32*24 => 768

Now, total work = LCM( 384,768 ) => 768

So, Efficiency of men = 2 & Efficiency of women = 1

Quote:
Sixteen men and sixteen women started working for twelve days.

Work completed = (16*2 + 16*1 )12 => 576 units , Work left = 768 - 576 => 192

Quote:
How many more men are to be added to complete the work remaining work in 2 days?

$${(16+m)*2 + 16*1 }*2 = 192$$

Or, $$(16+m)*2 + 16 = 96$$

Or, $$(16+m) = 40$$

Or, $$m = 24$$

Thus, we need to add , 24 more men workers, answer must be (B) 24 men...
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Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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17 May 2017, 04:08
1
the question is done in two parts:

1) work rate comparison bw men and women
24 men ---- 16 days
1 man ----- 24x16
16 man ----- 24 days

32 women ---- 24 days
16 women --- 48 days

so men : women = 2 : 1
men will do double the work done by women

2) work remaining after 12 days, that needs to be done in 2 days

men need 24 days to finish the work. so in 12 days they will do half the job
m ---- 1/2

women need 48 days to finish the job, and in 12 days they will do 12/48 = 1/4 th of the work

w----- 1/4

total work done in 12 days = m+w = 1/2 + 1/4 = 3/4
balance = 1/4 of work

In other words 1/4 * 24 =6 days of work for 16 men and 16 women

how many additional men required to finish in two days :
1/2 of work is done by 16 men
so 1/4 of work will be done by 8 men
total = 16+8= 24 men
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Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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18 May 2017, 20:05
Chemerical71 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

We are given that the rate of 24 men is 1/16, so the rate of each man is (1/16)/24 = 1/(16 x 24). Similarly, we are given that the rate of 32 women is 1/24, so the rate of each woman is (1/24)/(32) = 1/(24 x 32). Now we can find the fraction of the job that is completed by 16 men and 16 women in one day.

16 x 1/(16 x 24) + 16 x 1/(24 x 32)

1/24 + 1/(24 x 2)

2/48 + 1/48

3/48 = 1/16

We see that 16 men and 16 women can complete 1/16 of the job in one day, so they can complete 12 x 1/16 = 12/16 = 3/4 of the job in 12 days.

We can let m be the number of additional men who must be added to complete the job in two more days. Since we have 1 - 3/4 = 1/4 of the job left and it needs to be completed in two2 more days, each day they need to complete (1/4)/2 = 1/8 of the job. Thus, we can create the following equation to solve for m:

(16 + m) x 1/(16 x 24) + 16 x 1/(24 x 32) = 1/8

1/24 + m/(16 x 24) + 1/48 = 1/8

Multiplying the above equation by 48, we have:

2 + m/8 + 1 = 6

m/8 = 3

m = 24

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Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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18 May 2017, 21:14
I will attempt this in a similar way as Ashudhall.

In these kind of questions, its a good idea sometimes to take total units of work as the LCM of all the days and number of people given. Because we need a number which is divisible by all of those. Let me explain.

LCM of 24, 16, 32 and 24 is 96. So lets assume total work to be done as 96 units.
24 men can do 96 units work in 16 days
So 24 men can do in 1 day = 96/16 = 6 units of work.
So 1 man can do in 1 day = 6/24 = 1/4 units of work

Also, 32 women can do 96 units of work in 24 days
So 32 women can do in 1 day = 96/24 = 4 units of work
So 1 woman can do in 1 day = 4/32 = 1/8 units of work

Thus, 16 men and 16 women can do in 1 day = 16*1/4 + 16*1/8 = 6 units of work
As per the question, the work has to be completed in 14 total days
In 14 days, these 16 men and 16 women would have completed = 14*6 = 84 units of work

Remember that total units of work are 96.
Remaining work units = 96-84 = 12 units

If 'n' extra men are employed to finish off these 12 units in 2 days, it means these 'n' men finish 6 units in 1 day
We know that 1 man does 1/4 units work in 1 day
Therefore, no of men required 'n' = 6/(1/4) = 24

So 24 extra men are required. Answer is B
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Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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06 Jun 2017, 01:03
Chemerical71 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

1. 1 man takes 384 days and 1 woman takes 768 days
2. (no.of days worked by men* no.of men)/(time taken for a man working alone) +
(no.of days worked by additional men * no.of additional men )/(time taken for a man working alone)+
(no.of days worked by women* no.of women)/(time taken for a woman working alone) = 1
3. (14*16)/384 + (2*x)/384 + (14*16)/768=1
We get x=24
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Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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14 Jan 2018, 12:54
Hi All,

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

GMAT assassins aren't born, they're made,
Rich
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Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c   [#permalink] 14 Jan 2018, 12:54

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# Twenty-four men can complete a work in sixteen days.Thirty-two women c

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