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

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It takes 6 days for 3 women and 2 men working together to [#permalink]

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19 Aug 2009, 12:33
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 Jul 2013, 07:11, edited 2 times in total.
Edited the question.
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Re: Time n Work Problem [#permalink]

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19 Aug 2009, 15:00
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virtualanimosity wrote:
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?
1] 3 times
2] 4 times
3] 5 times
4] 6 times
5] 7 times

Clear D:

x: days 9 women doing the job --> 1 woman works W=1/9x per day
x-5: days 3 men doing the job --> 1 man works M=1/[3*(x-5)] per day

The answer to the question is: M/W

And, how much is x?

As per first data:

2*M+3*W=1/6
You can solve x, and obtain 2 values, 10 and 1 (1 is impossible because that would imply that the 3 men take -4 days), so x=10. So M/W=6 times
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Re: Time n Work Problem [#permalink]

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19 Jul 2010, 00:10
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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?
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Re: Time n Work Problem [#permalink]

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19 Jul 2010, 09:44
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nonameee wrote:
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?

Below is another solution which is a little bit faster.

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

Let one woman complete the job in $$w$$ days and one man in $$m$$ days. So the rate of 1 woman is $$\frac{1}{w}$$ job/day and the rate of 1 man is $$\frac{1}{m}$$ job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: $$\frac{3}{w}+\frac{2}{m}=\frac{1}{6}$$.

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

Solving: $$m=15$$ and $$w=90$$. $$\frac{w}{m}=6$$.

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Re: Time n Work Problem [#permalink]

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19 Jul 2010, 12:05
Bunuel wrote:
nonameee wrote:
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?

Below is another solution which is a little bit faster.

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

Let one woman complete the job in $$w$$ days and one man in $$m$$ days. So the rate of 1 woman is $$\frac{1}{w}$$ job/day and the rate of 1 man is $$\frac{1}{m}$$ job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: $$\frac{3}{w}+\frac{2}{m}=\frac{1}{6}$$.

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

Solving: $$m=15$$ and $$w=90$$. $$\frac{w}{m}=6$$.

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...
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Re: Time n Work Problem [#permalink]

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19 Jul 2010, 12:25
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AndreG wrote:
Bunuel wrote:
nonameee wrote:
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?

Below is another solution which is a little bit faster.

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

Let one woman complete the job in $$w$$ days and one man in $$m$$ days. So the rate of 1 woman is $$\frac{1}{w}$$ job/day and the rate of 1 man is $$\frac{1}{m}$$ job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: $$\frac{3}{w}+\frac{2}{m}=\frac{1}{6}$$.

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

Solving: $$m=15$$ and $$w=90$$. $$\frac{w}{m}=6$$.

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...

Let one woman complete the job in $$w$$ days and one man in $$m$$ days.

First equation:
It takes 6 days for 3 women and 2 men working together to complete a work:
As the rate of 1 woman is $$\frac{1}{w}$$ job/day, then the rate of 3 women will be $$\frac{3}{w}$$ job/day. As the rate of 1 man is $$\frac{1}{m}$$ job/day, then the rate of 2 men will be $$\frac{2}{m}$$ job/day. Combined rate of 3 women and 2 men in one day will be: $$\frac{3}{w}+\frac{2}{m}$$ job/day.

As they do all the job in 6 days then in 1 day they do 1/6 of the job, which is combined rate of 3 women and 2 men --> $$\frac{3}{w}+\frac{2}{m}=\frac{1}{6}$$.

Second equation:
3 men would do the same work 5 days sooner than 9 women:
As 1 man needs $$m$$ days to do the job 3 men will need $$\frac{m}{3}$$ days to do the job. As 1 woman needs $$w$$ days to do the job 9 women will need $$\frac{w}{9}$$ days to do the job. 3 men would do the same work 5 days sooner means that 3 men will need 5 less days to do the job, hence $$\frac{m}{3}$$ is 5 less than $$\frac{w}{9}$$ --> $$\frac{m}{3}+5=\frac{w}{9}$$.

Hope it's clear.
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Re: Time n Work Problem [#permalink]

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19 Jul 2010, 12:28
now i got it!

was confused, THANKS!
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Re: Time n Work Problem [#permalink]

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22 Jul 2010, 03:28
sam2010 wrote:
Bunel-I got a quadratic equation while solving these two eqn. Is there a simple way of solving them?

I also got quadratic equation ($$m^2-3m-180=0$$) and it wasn't too hard to solve (discriminant would be perfect square $$d=3^3+4*180=729=27^2$$) --> $$m=-12$$ or $$m=15$$.
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Re: Time n Work Problem [#permalink]

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24 Jan 2011, 09:20
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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
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Re: Time n Work Problem [#permalink]

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06 Mar 2011, 09:42
3
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virtualanimosity wrote:
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?
1] 3 times
2] 4 times
3] 5 times
4] 6 times
5] 7 times

Let women do $$w$$ units of work per day and men do $$m$$ units of work per day, then question asks, what is m/w

Total units of work to be done = $$6*(3*w+2*m)$$

Time taken by 9 women to do this work on their own = $$6*(3*w+2*m)$$/$$(9*w)$$ = $$2 + 4/3*m/w$$

Time taken by 3 men to do this work on their own = $$6*(3*w+2*m)/(3*m)$$ = $$6/(m/w) + 4$$

Let m/w be x

then we know

$$2 + (4/3)*x -6/x -4 = 5$$

or

$$(4/3)*x - 6/x= 7$$

Now substituting for x from choices will quickly give us x = 6 so D

I like this as it reduces quickly to the required form of m/w and it obviates the need for a quadratic equation and also lest w and m remain in numerator most of the time
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Re: Time n Work Problem [#permalink]

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06 Mar 2011, 18:40
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.

Bunuel wrote:
nonameee wrote:
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?

Below is another solution which is a little bit faster.

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

Let one woman complete the job in $$w$$ days and one man in $$m$$ days. So the rate of 1 woman is $$\frac{1}{w}$$ job/day and the rate of 1 man is $$\frac{1}{m}$$ job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: $$\frac{3}{w}+\frac{2}{m}=\frac{1}{6}$$.

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

Solving: $$m=15$$ and $$w=90$$. $$\frac{w}{m}=6$$.

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Re: Time n Work Problem [#permalink]

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06 Mar 2011, 20:20
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Let 9W take x days to complete a job

9W-> x days
1W-> 9x days

3M-> (x-5) days
1M-> (x-5)3 days

3W and 2M complete a job in 6 days;

3W-> 9x/3=3x days
2M-> (x-5)3/2 days

3W-> 1 day -> 1/(3x) work
2M-> 1 day -> 2/(3x-15) work

$$\frac{1}{3x}+\frac{2}{3x-15} = \frac{1}{6}$$

Solving;
$$x^2-11x+10=0$$

x=10
x=-1
Negative value not possible.
x=10

1W takes 9x days = 9*10 days = 90 days
1M takes (x-5)3 days = 5*3 = 15 days

M is 6 times faster.

Ans: "4"

gmat1220:

the LHS and RHS should represent same units
Days to days
or
Work to Work

Assuming M work/day for 1 Man
6M work in 6 days
1 Man -> 6M work
2 Men -> 12M work

and W work/day for 1 Woman
6 Women work in 6 days
1 Woman-> 6W work
3 Woman-> 18W work

Work done by 2 Men in 6 days+Work done by 3 Women in 6 days = 1 Work
12M+18W=1----- EQ1.....

3 Men complete 1 work 5 days sooner than 9 Women
Let's see how many days will it take to complete 1 work for 3 Men and 9W independently.

1 Man ->1 day-> M work
M work-> 1 day
1 work-> 1/M days
3 Men -> 1/(3M) days

1 Woman ->1 day-> W work
W work-> 1 day
1 work-> 1/W days
9 Women -> 1/(9W) days

1/(3M) = (1/(9W)) - 5 ;;; ----- EQ2.....Here we have compared days

Solving both equations EQ1 and EQ2 through substitution, we get

$$(90*9)W^2-90W-9W+1=0$$
$$(90W-1)(9W-1)=0$$

W=1/90 and M=1/15
or
W=1/9 and M=-1/12

-ve value is not possible. Thus

Rate/day for W= 1/90
Rate/day for M= 1/15

M is 6 times W.

We can solve it using any method; we just need to make sure the RHS and LHS are comparable.
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Re: Time n Work Problem [#permalink]

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06 Mar 2011, 21:08
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virtualanimosity wrote:
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?
1] 3 times
2] 4 times
3] 5 times
4] 6 times
5] 7 times

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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Re: Time n Work Problem [#permalink]

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06 Mar 2011, 21:45
Let 1 man comlete the work in M days and 1 woman complete the work in W days.

So 1 Man in 1/M part of work in 1 day and 1/W part of work in 1 day

1 man in 6 days -> 6/M part of work; 6/W part of work

2 M in 6 days - 12/M ; 3 W in 6 days - 18/W part of work

2/M + 3/W = 1/6 or 12/M + 18/W = 1

=> 2/M = 1/6 - 3/W

=> 1/M = 1/12 - 3/2W

Work done by 3 men in 1 day = 3/M and by 9 women = 9/w

So the complete work is done by 3 men in 1/3/M = M/3

1/9/W - 1/3/M = 5

w/9 - M/3 = 5

=> w/9 - 5 = M/3 => 3/M = 9/(w - 45)

1/12 - 3/2W = 3/(w-45)

(w - 18)/12W = 3/(w - 45)

w^2 - 45w + 810 -18w = 36w

w^2 - 99w + 810 = 0

So w = 90 and M = 15
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Re: Time n Work Problem [#permalink]

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04 Apr 2011, 18:14
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

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Re: Time n Work Problem [#permalink]

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11 Jul 2011, 06:11
The way we choose the variant for the equation is important. that way can make a simple equation or harder equation.

I choose the variant the way which leads to very hard equation which I can not solve.

So, the key is to choose the variant the way kudo choose and get the easier equation to do.
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Re: Time n Work Problem [#permalink]

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20 Nov 2011, 12:05
Bunuel wrote:
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

Let one woman complete the job in $$w$$ days and one man in $$m$$ days. So the rate of 1 woman is $$\frac{1}{w}$$ job/day and the rate of 1 man is $$\frac{1}{m}$$ job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: $$\frac{3}{w}+\frac{2}{m}=\frac{1}{6}$$.

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

Solving: $$m=15$$ and $$w=90$$. $$\frac{w}{m}=6$$.

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..
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Re: Time n Work Problem [#permalink]

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15 Sep 2012, 02:59
Bunuel wrote:
sam2010 wrote:
Bunel-I got a quadratic equation while solving these two eqn. Is there a simple way of solving them?

I also got quadratic equation ($$m^2-3m-180=0$$) and it wasn't too hard to solve (discriminant would be perfect square $$d=3^3+4*180=729=27^2$$) --> $$m=-12$$ or $$m=15$$.

Hello Bunuel,

I honestly did not understand the simplification...i normally go wrong this part of the problem. Kindly can u suggest more simplified method to do during a time-constraint?

Regards
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Re: Time n Work Problem [#permalink]

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15 Sep 2012, 10:06
Bunuel wrote:
sam2010 wrote:
Bunel-I got a quadratic equation while solving these two eqn. Is there a simple way of solving them?

I also got quadratic equation ($$m^2-3m-180=0$$) and it wasn't too hard to solve (discriminant would be perfect square $$d=3^3+4*180=729=27^2$$) --> $$m=-12$$ or $$m=15$$.

Just a smal typo: in the discriminant, it should be $$3^2$$ and not $$3^3.$$
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Re: It takes 6 days for 3 women and 2 men working together to [#permalink]

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15 Sep 2012, 10:53
virtualanimosity wrote:
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

The fastest and easiest way to solve this question was already proposed by IanStewart.

I am trying another algebraic approach.

Denote by $$W$$ the rate of a woman, by $$M$$ that of a men, and by $$T$$ the time it takes 9 women to complete the work.
We have the following equations:
$$6(3W + 2M) = 9WT = 3M(T-5)$$, or, after reducing by 3, $$2(3W + 2M) = 3WT = M(T - 5).$$
We are looking for the ratio $$M/W$$ which we can denote by $$n.$$ Substituting in the above equations $$M = nW,$$ we can write:
$$2(3W + 2nW) = 3WT = nW(T - 5).$$

Divide through by $$W,$$ so $$6 + 4n = 3T = nT - 5n.$$ Solving for $$T$$ (equality between the last two expressions) we obtain $$T=\frac{5n}{n-3}.$$
Taking the equality of the first two expressions, we get $$6+4n=\frac{3\cdot{5}n}{n-3}.$$
From the possible answer choices we can deduce that $$n$$ must be a positive integer.
We need $$\frac{15n}{n-3}$$ to be a positive integer. We can see that $$n$$ cannot be odd and it must be greater than 3.
We have to choose between B and D.
Only $$n = 6$$ works.

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Re: It takes 6 days for 3 women and 2 men working together to   [#permalink] 15 Sep 2012, 10:53

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2 3 men and 3 women need to be seated in 2 rows with 3 chairs 5 28 Sep 2010, 05:47
6 A work crew of 4 Men takes 5 days to complete one-half of a 10 13 Mar 2010, 08:24
19 It takes 6 days for 3 women and 2 men working together to 13 12 Mar 2010, 22:33
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