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

Question

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

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

KarishmaB · Accepted Answer

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) Check this video for the basics of work rate: https://youtu.be/88NFTttkJmA

ScottTargetTestPrep · Answer

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

saswata4s · Answer

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 .

Answer B.

This is not a SUB-600 level question.

Chemerical71 · Answer

Then, extra men required in next 2 days: (24*16)/(2*8) = 24 . please explain this step again. :-D

BillyZ · Answer

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).

KrishnakumarKA1 · Answer

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

warriorguy · Answer

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)

KarishmaB · Answer

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 Check out this blog post on work rate: https://anaprep.com/arithmetic-work-rat ... variation/

gmatexam439 · Answer

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

Answer: D

ashudhall · Answer

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

Sent from my ONEPLUS A3003 using  GMAT Club Forum mobile app

gmathopeful19 · Answer

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 
   Posted from my mobile device

stonecold · Answer

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*   = W/4

Solving this we get => x=24

Hence B.

SMASH THAT B.

Looking forward to the OE.

stonecold · Answer

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  =1/4 
x=40
Hence additional men required => 40-16 => 24

Smash that B.

Abhishek009 · Answer

So, Total mandays = 24*16 => 384

So, Total womandays = 32*24 => 768

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

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

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

{(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...

hanyhamdani · Answer

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

ScottTargetTestPrep · Answer

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

Answer: B

amanvermagmat · Answer

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

SVaidyaraman · Answer

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

EMPOWERgmatRichC · Answer

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

Final Answer:  B

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

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