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.How many times does the output of a man exceed that of a woman?

A. 3 times
B. 4 times
C. 5 times
D. 6 times
E. 7 times

Guys, even if you know the solution right away, it takes several minutes (definitely more than 3) to just write it down to find the answer. Is it a real GMAT question? Can something like that be expected on the real test?

Hm, i got stuck cuz I got something a little different:
YOURS: 3 men would do the same work 5 days sooner than 9 women --> \frac{m}{3}+5=\frac{w}{9}.

MINE: 3 men would do the same work 5 days sooner than 9 women --> \frac{3}{m}=\frac{9}{w}+5

In the above equation you also have for 2 men: \frac{2}{m} - so why do u suddenly use the reciprocal? And why don't we add the 5 to women, because they take longer, hence their side is smaller...

now i got it!

was confused, THANKS!

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

Bunuel
I saw both the solutions. However, please tell me where I go wrong -

Lets assume M work / day and W work / day are the rates of men and women respectively.

First stimulus -It takes 6 days for 3 women and 2 men working together to complete a work
Second stimulus - 3 men would do the same work 5 days sooner than 9 women

1/(3W) + 1/(2M) = 6
1/(9W) - 1/(3M) = 5

I am getting negative value of M Please correct.

I received a PM asking me to respond. First, this is definitely not a realistic GMAT question. For one thing, it's horribly written (the phrase 'to complete a work' is not English, the question should read '*By* how many times...', the question needs to make clear that each man works at the same rate, as does each woman, the word 'sooner' is non-idiomatic, the word 'output' is misused, etc). For another, it's terribly contrived, and altogether tedious if you take any normal approach; I don't see any direct way to solve that will allow you to avoid a quadratic equation. Real GMAT questions are never designed in such a way, so you can confidently move on to better material and ignore this question (incidentally, where is it from?).

While it isn't especially fast either, you can work backwards from the answers here relatively easily. This might at least be less confusing for some than a direct (algebraic) approach. Say we get 1 unit of work per woman per day. If you test, say, answer C, we'd then get 5 units of work per man per day. The job would then require 6(3 + 2*5) = 78 units of work. Notice that, to find how long it will take 9 women to do the job, we'll need to get an integer when we divide 78 by 9, so C cannot be right. If you move next to D, we have 6 units of work per man per day, and the job requires 6(3 + 2*6) = 90 units of work. Thus 9 women do the job in 10 days, and 3 men would do the job in 90/(6*3) = 5 days, so D is correct.
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3/W + 2/M = 1/6




Let 9 W complete in X days

So 1 W will take 9X days

And 3 M will take (X-5) days

So 1 M will take 3(X-5) days

3/9X + 2/3(X-5) = 1/6

=> 2/X + 4/(X-5) = 1

=> 2x - 10 + 4x = x^2 - 5x

=> x^2 - 11x + 10 = 0

=> x^2 -10x - x + 10 = 0

=> x(x - 10) - 1(x - 10) = 0

So x = 10, else x-5 is -ve

So 1 M = 3 * 5 = 15, 1 W = 90

W/M = 6

Hence answer - D
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Bunuel,

When the question says "3 men would do the same work 5 days sooner than 9 women".

Do the colored words refer to the word work mentioned in the previous sentence; Total Work to complete the job?

I am a bit confused..

Just a smal typo: in the discriminant, it should be 3^2 and not 3^3.
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