It takes 6 days for 3 women and 2 men working together to

We can let the number of days for 1 man to finish the work = m and that for 1 woman = w. Thus, the rate of 1 man = 1/m and the rate of 1 woman = 1/w.

Since it takes 6 days for 3 women and 2 men working together to complete the work, we have:

6(3/w + 2/m) = 1

Since 3 men would do the same work 5 days sooner than 9 women, we have:

1/(3/m) + 5 = 1/(9/w)

m/3 + 5 = w/9

Multiplying the above by 9, we have:

3m + 45 = w

Substituting this into 6(3/w + 2/m) = 1, we have:

6(3/(3m + 45) + 2/m) = 1

6(1/(m + 15) + 2/m) = 1

Multiplying the above by m(m + 15), we have:

6m + 12(m + 15) = m(m + 15)

6m + 12m + 180 = m^2 + 15m

m^2 - 3m - 180 = 0

(m - 15)(m + 12) = 0

m = 15 or m = -12

Since m can’t be negative, m = 15. So w = 3(15) + 45 = 90. We see that it takes a man 15 days to complete the work but 90 days for a woman to complete the same work. So a man’s output is 6 times the output of a woman.

Answer: D

Please find attached the solution

3w+2m= 1/6 (in one day )

NEXT: 3 men would do the same work 5 days sooner than 9 women , SO let X be the job done by woman and let x-5 be the work done by men


HENCE: \(\frac{1}{x}- \frac{1}{(x-5)} = \frac{x-5-x}{x(x-5)}\) i.e \(\frac{-5}{x(x-5)}\) (i know i got negative in numerator but still continued solving further )


\(\frac{-5}{x(x-5)}\) = \(\frac{1}{6}\) cross multiply

\(x(x-5)=-30\)

\(x\) = \(\frac{-30}{x(x-5)}\) now if i divide -30 by -5 i get 6. this was my solution to correct answer


Bunuel, pushpitkc generis do you think my solution is correct ?

Hello all,

I couldn't solve this question within time. But i did attempt it the following manner and got the answer right. Can someone tell me if this approach is correct/incorrect?

Let the work be W.

Now, based on the data provided
- one man can do 1/3 of W
- one woman can do 1/9 of W

Here i am now assuming a number for W - let's say the work needed to be done is eating 27 pies. i.e. W=27

So one man can eat 9 pies and one woman can eat 3 pies.

Because the question asks How many times does the output of a man exceed that of a woman?, I have understood this as Output of a man (9 pies) is x more than output of a woman (3 pies).
so 9 = 3+x therefore, X=6.

Let me know if this makes sense or I was just lucky to get the answer right (won't work all the time)

Hi Bunuel,

I have no trouble setting up the two equations. However, I don’t know how to solve them quickly and efficiently since w and m are found in the denominators of the 1st equation and in the numerators of the 2nd equation. Please help! Thank you so much




Posted from my mobile device

Rurugu You can refer to my method as well if it looks any easier to you.

Link is here...


https://gmatclub.com/forum/it-takes-6-d ... l#p2167832

Solving quadratic equations, especially when they involve large numbers and need a lot of calculations to form the equation in the first place, is quite time-consuming and the likelihood of calculation errors is also quite high. I doubt whether problems like this can be solved within the GMAT time-frame in the conventional manner. However, there is a much quicker way of solving this problem with a bit of logic and by taking a few hints from the answer choices:

Let the time taken by 3 men to do the work be 'x' days.
Then, the time taken by 9 women to do the work is (x+5) days which means time taken for 3 women will be 3(x+5) days. If M and W are the speeds or rates of men and women respectively, then:
M/W = 3(x+5)/x. In other words, a man is 3(x+5)/x times faster than a woman.
3(x+5)/x = 3 + 15/x. Since all the answer options are whole numbers 'x' must be a factor of 15, i.e. either 3, 5 or 15. It can't be 3 because that would make a man 8(3+5) times faster (7 is the highest option).
x=15 would mean that 3 men complete the work in 15 days or 5 men complete in (3*15)/5=9 days. But we know that 3 women and 2 men complete in 6 days. Since men are faster than women so, if we substitute the 3 women by 3 men and we have 5 men working on the job it can be finished in less than 6 days. So 'x' cannot be 15 which leaves only 5 as the only possible value for 'x'. So a man is (3 + 15/5) = 3 +3 = 6 times faster than a woman.

Ans: D

given total work
5x/6=1/6
or say x=1/5
so for 3 men = 5+ 9 women
3*1/5*x = 5+9/5
3x=18
i.e 6 times
IMO D

Archit3110

Could you please explain the assumptions underlying your answer? For example, what does 'x' stand for? I am a bit confused because first you got
x=1/5 and then you got x=6. A detailed explanation would help us understand the process through which you arrived at your answer. Thanks.

We can let m = the number of days a man can complete the work by himself and w = the number of days a woman can complete the work by herself. Thus, 1/m = the rate of a man, and 1/w = the rate of a woman.

We can create the equations

6(3 x 1/w + 2 x 1/m) = 1

and

1/(3 x 1/m) = 1/(9 x 1/w) - 5

Simplifying the first equation, we have:

3/w + 2/m = 1/6

Multiplying the equation by 6wm, we have:

18m + 12w = mw

Simplifying the second equation, we have:

m/3 = w/9 - 5

Multiplying the equation by 9, we have:

3m = w - 45

3m + 45 = w

Substituting this in 18m + 12w = mw, we have:

18m + 12(3m + 45) = m(3m + 45)

18m + 36m + 540 = 3m^2 + 45m

3m^2 - 9m - 540 = 0

m^2 - 3m - 180 = 0

(m - 15)(m + 12) = 0

m = 15 or m = -12

Since m can’t be negative, m = 15. Hence, w = 3(15) + 45 = 90. We see that a man’s rate is 6 times that of a woman’s rate since the number of days a man can complete the job is only 1/6 of the number of days a woman can complete the job.

Answer: D

maelstroem wrote:
First set : 3/w+2/m=1/6
Second set: 3/m = 1/x and 9/w=1/(x+5)
==> 1/m = 1/3x and 1/w = 1/9(x+5)
Enter in first equation and solve for x
1/(3x+15) + 2/3x = 1/6
simplify => x^2-x-20=0
solve for x : x=(1 +- (1+80)^,5)/2= (1+- 9)/2.
X can only be positive ==> x= 5
enter in 2nd set ==> 3/m=1/5 and 9/w=1/10 => 3/2m=9/w => m/w=1/6

I did it in a similar manner. I assumed that 3 men can complete in 'x' days which means that 9 women can complete in (x+5) days and, working forward from there, got the same equation:
x^2 - x - 20 = 0. What I want to point out here is that in this type of quadratic equation where factorization is possible it is quicker to factorize:

x^2 -x -20 = 0...> x^2 - 5x + 4x - 20 = 0...> x(x-5) + 4(x-5) = 0...> (x-5)(x+4) = 0. x=5

Given: It takes 6 days for 3 women and 2 men working together to complete a work. 3 men would do the same work 5 days sooner than 9 women.
Asked: How many times does the output of a man exceed that of a woman?

Let a man complete the work in m days and a women complete the same work in w days.

It takes 6 days for 3 women and 2 men working together to complete a work.
3/w + 2/m = 1/6

3 men would do the same work 5 days sooner than 9 women.
m/3 + 5 = w/9

m = 15; w = 90 is the solution

IMO D

Can you write out the bolded "solving" portion below? Bunuel

+1

I just cant get it right. I understand the concept until it comes to solving the equation.


I get x = 18 and y = 54. I would appreciate if someone could show how to solve this to arrive at the correct answer.

Bunuel, I think the answer to this question should be 5 and not 6. As it is worded, the question asks "How many times does the output of a man exceed that of a woman?" When we get m/w as 6, it means that "the output of a man is 6 times that of a woman"

To calculate how many times 6 exceeds 1, I think what we should be doing is (6-1)/1, can you please suggest if this is right?

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