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If 12 men and 16 women can do a piece of work in 5 days and

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Re: If 12 men and 16 women can do a piece of work in 5 days and  [#permalink]

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New post 21 Feb 2018, 00:49
Suppose 1 man takes m days and 1 woman takes w days to complete the work.

So, in 1 day, a man would do 1/m and a woman would do 1/w work

In 5 days, 12 men and 16 women would do 5*(12/m + 16/m) work

Similarly, in 4 days, 13 men and 24 women would do 4*(13/m + 24/w) work

But this is the total work. So,

5*(12/m + 16/m) = 4*(13/m + 24/w)
Solving, we get w=2m

Since 12 men and 16 women can do a piece of work in 5 days

So, from this we can find out that the total amount of work = 60 man-days + 80 women-days = 200 women-days.

7 men and 10 women = 14 women + 10 women= 24 women

So, number of days = 200/24 = 8.3 days.
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Re: If 12 men and 16 women can do a piece of work in 5 days and  [#permalink]

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New post 19 Sep 2018, 05:33
GMATinsight wrote:
smcgrath12 wrote:
If 12 men and 16 women can do a piece of work in 5 days and 13 men and 24 women can do it in 4 days, how long will 7 men and 10 women take to do it?

(A) 4.2 days
(B) 6.8 days
(C) 8.3 days
(D) 9.8 days
(E) 10.2 days



Answer: Option C

Please find solution as attached.


Dear GMATinsight

I'm interested in your solution but I see that the equation you use here contradicts (as I understand) with other problem in which you used the same equation.

In the equation: (M*T)/w = constant, I understand M as pure manpower. However, in you solution it is seems you use it as rate expression (12M+16W) multiplied by days (5). I have big confusion between abbreviation and its real usage in the equation.

Can you elaborate more ?

Thanks in advance
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Re: If 12 men and 16 women can do a piece of work in 5 days and  [#permalink]

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New post 19 Sep 2018, 05:45
GMATinsight wrote:
smcgrath12 wrote:
If 12 men and 16 women can do a piece of work in 5 days and 13 men and 24 women can do it in 4 days, how long will 7 men and 10 women take to do it?

(A) 4.2 days
(B) 6.8 days
(C) 8.3 days
(D) 9.8 days
(E) 10.2 days



Answer: Option C

Please find solution as attached.


Dear GMATinsight

I liked you solution. But I do not understand the abbreviation used in the equation compared to other problems in which you used this equation.

In the equation (M*T)/w, I understand 'M' as pure manpower, but it seems you used (12M+16w) as rate multiplied by # of days (5) which work equation and at end Work/Work. I have real confusion about the abbreviations used in the equation and the solution.

Can you elaborate please ?
Thanks in advance
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Re: If 12 men and 16 women can do a piece of work in 5 days and  [#permalink]

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New post 20 Sep 2018, 04:31
1
Mo2men wrote:
GMATinsight wrote:
smcgrath12 wrote:
If 12 men and 16 women can do a piece of work in 5 days and 13 men and 24 women can do it in 4 days, how long will 7 men and 10 women take to do it?

(A) 4.2 days
(B) 6.8 days
(C) 8.3 days
(D) 9.8 days
(E) 10.2 days



Answer: Option C

Please find solution as attached.


Dear GMATinsight

I liked you solution. But I do not understand the abbreviation used in the equation compared to other problems in which you used this equation.

In the equation (M*T)/w, I understand 'M' as pure manpower, but it seems you used (12M+16w) as rate multiplied by # of days (5) which work equation and at end Work/Work. I have real confusion about the abbreviations used in the equation and the solution.

Can you elaborate please ?
Thanks in advance


Mo2men

M = manpower/Machine power here total manpower is 12 Men and 16 women hence wrote it as 12M+16W
T = Time that Man/machine power will take to finish the work
W = Amount of work to be finished

M is directly proportional to W and
M is inversely Proportional to T
hence, M = k(W/T)
CONCEPT: \(\frac{(Machine_Power * Time)}{Work} = Constant\)
i.e. \(\frac{(M_1 * T_1)}{W_1} = \frac{(M_2 * T_2)}{W_2}\)

Hope this explains your doubt
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If 12 men and 16 women can do a piece of work in 5 days and  [#permalink]

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New post 20 Sep 2018, 04:59
GMATinsight wrote:

Mo2men

M = manpower/Machine power here total manpower is 12 Men and 16 women hence wrote it as 12M+16W
T = Time that Man/machine power will take to finish the work
W = Amount of work to be finished

M is directly proportional to W and
M is inversely Proportional to T
hence, M = k(W/T)
CONCEPT: \(\frac{(Machine_Power * Time)}{Work} = Constant\)
i.e. \(\frac{(M_1 * T_1)}{W_1} = \frac{(M_2 * T_2)}{W_2}\)

Hope this explains your doubt


Dear GMATinsight

Thanks for your care to reply. I still have confusion. Let me try to explain.

The highlight past is comprise of 12M so it is 12 multiplied by variable M and 16 multiplied by variable W and hence you concluded a relation between them. I do not know why you multiplied by those variables whereas the original formula (as stated by you and your solution in other problems like below) contains only machine/man power without multiplication in any variables). Please look below

https://gmatclub.com/forum/if-it-takes- ... s#p1729381

While I understood your solutions in the link, I could not comprehend what you provided for the question at hand.

I hope you understand where my confusion is.
Thanks in advance
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Re: If 12 men and 16 women can do a piece of work in 5 days and  [#permalink]

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New post 20 Sep 2018, 05:14
Mo2men wrote:
GMATinsight wrote:

Mo2men

M = manpower/Machine power here total manpower is 12 Men and 16 women hence wrote it as 12M+16W
T = Time that Man/machine power will take to finish the work
W = Amount of work to be finished

M is directly proportional to W and
M is inversely Proportional to T
hence, M = k(W/T)
CONCEPT: \(\frac{(Machine_Power * Time)}{Work} = Constant\)
i.e. \(\frac{(M_1 * T_1)}{W_1} = \frac{(M_2 * T_2)}{W_2}\)

Hope this explains your doubt


Dear GMATinsight

Thanks for your care to reply. I still have confusion. Let me try to explain.

The highlight past is comprise of 12M so it is 12 multiplied by variable M and 16 multiplied by variable W and hence you concluded a relation between them. I do not know why you multiplied by those variables whereas the original formula (as stated by you and your solution in other problems like below) contains only machine/man power without multiplication in any variables). Please look below

https://gmatclub.com/forum/if-it-takes- ... s#p1729381

While I understood your solutions in the link, I could not comprehend what you provided for the question at hand.

I hope you understand where my confusion is.
Thanks in advance


Mo2men

Let me attempt to answer this again

The relationship that I explained MT/W = Constant is applicable only if the work is of same nature in both scenarios and the Manpower also is of same nature in both scenario only their quantities differ.

When I say 12M+16W then I am considering the manpower of different nature hence it's important for me to use this relationship to determine the ratio of efficiencies of different manpowers.

Similarly if two machines of different types (e.g. old and new) are used together then it's paramount that we convert the machines into equivalent machines of one nature only.

12M refers to efficiency of 12 men and 16W refers to efficiency of 16 women here.
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Re: If 12 men and 16 women can do a piece of work in 5 days and  [#permalink]

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New post 20 Sep 2018, 07:58
smcgrath12 wrote:
If 12 men and 16 women can do a piece of work in 5 days and 13 men and 24 women can do it in 4 days, how long will 7 men and 10 women take to do it?

(A) 4.2 days
(B) 6.8 days
(C) 8.3 days
(D) 9.8 days
(E) 10.2 days

\(7\,\,{\text{men}}\,\, \cup \,\,\,{\text{10}}\,\,{\text{women}}\,\,\, - \,\,\,1\,\,{\text{work}}\,\,\,\, - \,\,\,?\,\,{\text{days}}\)

Is there a systematic way of dealing with this kind of problem, to be able to do it in a few minutes "naturally"?

Certainly! Let´s do it:

Let "task" be the fraction of this (piece of) work that one man can do in 1 day, hence:

\(1\,\,{\text{man}}\,\,\, - \,\,\,1\,\,{\text{day}}\,\,\,\, - \,\,\,1\,\,{\text{task}}\)

Let k (k>0) be the fraction of the "task" defined above that one woman can do in 1 day (where k may be between 0 and 1, or equal to 1, or greater), hence:

\(1\,\,{\text{woman}}\,\,\, - \,\,\,1\,\,{\text{day}}\,\,\, - k\,\,{\text{tasks}}\,\)

Now the long-lasting benefit of this "structure": everything else becomes easy and "automatic":

\(\left. \begin{gathered}
{\text{12}}\,\,{\text{men}} - \,\,\,5\,\,{\text{days}}\,\,\, - \,\,\,\,12 \cdot \,5 \cdot 1\,\,\,{\text{tasks}}\, \hfill \\
{\text{16}}\,\,{\text{women}} - \,\,\,5\,\,{\text{days}}\,\,\, - \,\,\,\,16 \cdot \,5 \cdot k\,\,\,{\text{tasks}}\,\,\, \hfill \\
\end{gathered} \right\}\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{question}}\,\,{\text{stem}}} \,\,\,\,5\left( {12 + 16k} \right)\,\,{\text{tasks}}\,\,\,\, = \,\,\,\,1\,\,{\text{work}}\,\,\,\,\left( * \right)\)

\(\left. \begin{gathered}
{\text{13}}\,\,{\text{men}} - \,\,\,4\,\,{\text{days}}\,\,\, - \,\,\,\,13 \cdot \,4 \cdot 1\,\,\,{\text{tasks}}\, \hfill \\
{\text{24}}\,\,{\text{women}} - \,\,\,4\,\,{\text{days}}\,\,\, - \,\,\,\,24 \cdot \,4 \cdot k\,\,\,{\text{tasks}}\,\,\, \hfill \\
\end{gathered} \right\}\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{question}}\,\,{\text{stem}}} \,\,\,\,4\left( {13 + 24k} \right)\,\,{\text{tasks}}\,\,\,\, = \,\,\,\,1\,\,{\text{work}}\,\,\,\,\left( {**} \right)\)

\(\left( * \right) = \left( {**} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,5\left( {12 + 16k} \right) = 4\left( {13 + 24k} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,k = \frac{1}{2}\)

\(?\,\,\,\,:\,\,\,\,\,\left. \begin{gathered}
\boxed{{\text{7}}\,\,{\text{men}}} - \,\,\,1\,\,{\text{day}}\,\,\, - \,\,\,\,7\,\,\,{\text{tasks}}\, \hfill \\
\boxed{{\text{10}}\,\,{\text{women}}} - \,\,\,1\,\,{\text{day}}\,\,\, - \,\,\,\,10 \cdot k = 5\,\,\,{\text{tasks}}\,\,\, \hfill \\
\end{gathered} \right\}\,\,\,\,\,\mathop \Rightarrow \limits^{\boxed{{\text{FOCUSED - GROUP}}}} \,\,\,\,\frac{{12\,\,{\text{tasks}}}}{{1\,\,\,{\text{day}}}}\,\,\,\,\left( {***} \right)\)

\(\left( * \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,5\left( {12 + 16 \cdot \frac{1}{2}} \right) = 100\,\,{\text{tasks}}\,\,{\text{ = }}\,\,{\text{1}}\,\,{\text{work}}\,\)

And we finish in "high style", using UNITS CONTROL, one of the most powerful tools of our method!

\(\left( {***} \right)\,\,\,\,?\,\,\, = \,\,\,100\,\,{\text{tasks}}\,\,\,\,\left( {\frac{{1\,\,\,\,{\text{day}}}}{{12\,\,{\text{tasks}}}}\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\,\, = \,\,\,\,\frac{{100}}{{12}} = \frac{{25}}{3} = \frac{{24 + 1}}{3} = 8\frac{1}{3}\,\,\,\,\left[ {{\text{days}}} \right]\)
Obs.: arrows indicate licit converter.



This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
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Re: If 12 men and 16 women can do a piece of work in 5 days and  [#permalink]

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New post 20 Sep 2018, 08:39
fskilnik wrote:
smcgrath12 wrote:
If 12 men and 16 women can do a piece of work in 5 days and 13 men and 24 women can do it in 4 days, how long will 7 men and 10 women take to do it?

(A) 4.2 days
(B) 6.8 days
(C) 8.3 days
(D) 9.8 days
(E) 10.2 days

\(7\,\,{\text{men}}\,\, \cup \,\,\,{\text{10}}\,\,{\text{women}}\,\,\, - \,\,\,1\,\,{\text{work}}\,\,\,\, - \,\,\,?\,\,{\text{days}}\)

Is there a systematic way of dealing with this kind of problem, to be able to do it in a few minutes "naturally"?

Certainly! Let´s do it:

Let "task" be the fraction of this (piece of) work that one man can do in 1 day, hence:

\(1\,\,{\text{man}}\,\,\, - \,\,\,1\,\,{\text{day}}\,\,\,\, - \,\,\,1\,\,{\text{task}}\)

Let k (k>0) be the fraction of the "task" defined above that one woman can do in 1 day (where k may be between 0 and 1, or equal to 1, or greater), hence:

\(1\,\,{\text{woman}}\,\,\, - \,\,\,1\,\,{\text{day}}\,\,\, - k\,\,{\text{tasks}}\,\)

Now the long-lasting benefit of this "structure": everything else becomes easy and "automatic":

\(\left. \begin{gathered}
{\text{12}}\,\,{\text{men}} - \,\,\,5\,\,{\text{days}}\,\,\, - \,\,\,\,12 \cdot \,5 \cdot 1\,\,\,{\text{tasks}}\, \hfill \\
{\text{16}}\,\,{\text{women}} - \,\,\,5\,\,{\text{days}}\,\,\, - \,\,\,\,16 \cdot \,5 \cdot k\,\,\,{\text{tasks}}\,\,\, \hfill \\
\end{gathered} \right\}\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{question}}\,\,{\text{stem}}} \,\,\,\,5\left( {12 + 16k} \right)\,\,{\text{tasks}}\,\,\,\, = \,\,\,\,1\,\,{\text{work}}\,\,\,\,\left( * \right)\)

\(\left. \begin{gathered}
{\text{13}}\,\,{\text{men}} - \,\,\,4\,\,{\text{days}}\,\,\, - \,\,\,\,13 \cdot \,4 \cdot 1\,\,\,{\text{tasks}}\, \hfill \\
{\text{24}}\,\,{\text{women}} - \,\,\,4\,\,{\text{days}}\,\,\, - \,\,\,\,24 \cdot \,4 \cdot k\,\,\,{\text{tasks}}\,\,\, \hfill \\
\end{gathered} \right\}\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{question}}\,\,{\text{stem}}} \,\,\,\,4\left( {13 + 24k} \right)\,\,{\text{tasks}}\,\,\,\, = \,\,\,\,1\,\,{\text{work}}\,\,\,\,\left( {**} \right)\)

\(\left( * \right) = \left( {**} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,5\left( {12 + 16k} \right) = 4\left( {13 + 24k} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,k = \frac{1}{2}\)

\(?\,\,\,\,:\,\,\,\,\,\left. \begin{gathered}
\boxed{{\text{7}}\,\,{\text{men}}} - \,\,\,1\,\,{\text{day}}\,\,\, - \,\,\,\,7\,\,\,{\text{tasks}}\, \hfill \\
\boxed{{\text{10}}\,\,{\text{women}}} - \,\,\,1\,\,{\text{day}}\,\,\, - \,\,\,\,10 \cdot k = 5\,\,\,{\text{tasks}}\,\,\, \hfill \\
\end{gathered} \right\}\,\,\,\,\,\mathop \Rightarrow \limits^{\boxed{{\text{FOCUSED - GROUP}}}} \,\,\,\,\frac{{12\,\,{\text{tasks}}}}{{1\,\,\,{\text{day}}}}\,\,\,\,\left( {***} \right)\)

\(\left( * \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,5\left( {12 + 16 \cdot \frac{1}{2}} \right) = 100\,\,{\text{tasks}}\,\,{\text{ = }}\,\,{\text{1}}\,\,{\text{work}}\,\)

And we finish in "high style", using UNITS CONTROL, one of the most powerful tools of our method!

\(\left( {***} \right)\,\,\,\,?\,\,\, = \,\,\,100\,\,{\text{tasks}}\,\,\,\,\left( {\frac{{1\,\,\,\,{\text{day}}}}{{12\,\,{\text{tasks}}}}\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\,\, = \,\,\,\,\frac{{100}}{{12}} = \frac{{25}}{3} = \frac{{24 + 1}}{3} = 8\frac{1}{3}\,\,\,\,\left[ {{\text{days}}} \right]\)
Obs.: arrows indicate licit converter.



This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.


I am really keen to ask, How did you do such a beautiful formatting??? :)
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Re: If 12 men and 16 women can do a piece of work in 5 days and  [#permalink]

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New post 20 Sep 2018, 08:44
This is a problem that the testmaker is trying to fool you into completing. You can definitely find the correct answer with math, however for most students this will take way too much time and is fraught with the opportunity for math errors. However, with 45 seconds or so of logic and estimation you can get this down to two possible answers. Strategically, this is a better choice here.

Here is the logic that you need to know:

Twice as many people complete the job in half of the time
Half of the people complete the job in twice of the time.

Pretty simple, right? Let's apply it to this question.

You know that 12 men and 16 women do the job in 5 days. So, 6 men and 8 women do the job in 10 days. Are 7 men and 10 women faster or slower? Well, faster! Eliminate E

You know that 13 men and 24 women do the job in 4 days. So, 6.5 men and 12 women do the job in 8 days. Are 7 men and 10 women faster or slower. While not as exact as the first estimation, probably a bit faster. A and B look pretty unlikely at this point.

So you are down to C and D. Is the answer closer to 8.3 or 9.8? From the 6.5 men and 12 women scenario, probably 8.3, which turns out to be the right answer.

You are likely to get only one or two work equation questions on test day. These questions typically involve a lot of math and are time consuming. Strongly consider opting for a logic approach on these questions. This approach will save you time that you may allocate to other questions.

Take a look at OG2019 PS 88. A very similar logic can be used to quickly eliminate c, d and e.
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If 12 men and 16 women can do a piece of work in 5 days and  [#permalink]

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New post 20 Sep 2018, 09:10
GMATinsight wrote:
I am really keen to ask, How did you do such a beautiful formatting??? :)


Hi, GMATInsight!

Thank you for your contact and interest in my solution.

It´s really just TEX inside the M symbols (that you find in the palette options).

Unfortunately, I cannot (by contract) mention any programs that I use to create my posts (formulas, figures, etc).

(All resources help us to offer a unique experience for our GMATH students, not only technically, but also visually...)

Thank you for your understanding!

Regards,
Fabio.
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Re: If 12 men and 16 women can do a piece of work in 5 days and  [#permalink]

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New post 23 Sep 2018, 11:37
1
Hi All,

We're told that 12 men and 16 women can do a piece of work in 5 days and 13 men and 24 women can do it in 4 days. We're asked how long it will take 7 men and 10 women to complete that same task. This question can be approached in a couple of different ways (some of which involve a lot of calculations). The answer choices are sufficiently 'spread out' that you can use a bit of 'ratio math' and a little logic to get to the correct answer.

We're going to focus on just the first piece of information: it takes 12 men and 16 women a total of 5 days to complete a task. If you were to DOUBLE the number of workers, then you would HALVE the amount of time (re: 24 men and 32 women would take 2.5 days to complete the task). If you were to HALVE the number of workers, then you would DOUBLE the amount of time that it takes to complete the task:

6 men and 8 women would take a total of 10 days to complete a task.

If we HALVE the number of workers again, we would again DOUBLE the amount of time needed to complete the task:

3 men and 4 women would take a total of 20 days to complete a task.

We're asked how long it would take 7 men and 10 women to complete that task. If we multiply the above 'work information' by 2.5, we get...

(2.5)(3) men and (2.5)(4 women) would take a total of 20/2.5 days to complete a task...
7.5 men and 10 women would take a total of 8 days to complete a task.
Notice how this is almost the exact question we were asked to solve for. The difference is that we're including an extra "1/2 of a man" in this calculation. With just 7 men (instead of 7.5 men), we would need slightly more than 8 days to complete the task. There's only one answer that matches....

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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Re: If 12 men and 16 women can do a piece of work in 5 days and  [#permalink]

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New post 24 Sep 2018, 04:07
EMPOWERgmatRichC wrote:
Hi All,

We're told that 12 men and 16 women can do a piece of work in 5 days and 13 men and 24 women can do it in 4 days. We're asked how long it will take 7 men and 10 women to complete that same task. This question can be approached in a couple of different ways (some of which involve a lot of calculations). The answer choices are sufficiently 'spread out' that you can use a bit of 'ratio math' and a little logic to get to the correct answer.

We're going to focus on just the first piece of information: it takes 12 men and 16 women a total of 5 days to complete a task. If you were to DOUBLE the number of workers, then you would HALVE the amount of time (re: 24 men and 32 women would take 2.5 days to complete the task). If you were to HALVE the number of workers, then you would DOUBLE the amount of time that it takes to complete the task:

6 men and 8 women would take a total of 10 days to complete a task.

If we HALVE the number of workers again, we would again DOUBLE the amount of time needed to complete the task:

3 men and 4 women would take a total of 20 days to complete a task.

We're asked how long it would take 7 men and 10 women to complete that task. If we multiply the above 'work information' by 2.5, we get...

(2.5)(3) men and (2.5)(4 women) would take a total of 20/2.5 days to complete a task...
7.5 men and 10 women would take a total of 8 days to complete a task.
Notice how this is almost the exact question we were asked to solve for. The difference is that we're including an extra "1/2 of a man" in this calculation. With just 7 men (instead of 7.5 men), we would need slightly more than 8 days to complete the task. There's only one answer that matches....

Final Answer:

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

Rich


Thanks EMPOWERgmatRichC for you nice and logic solution. However, I tried to apply same concept in another problem but reached wrong answer.

https://gmatclub.com/forum/2-men-and-3- ... l#p2137783

I tagged you in the other problem so that you can elaborate more.

Thanks
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Re: If 12 men and 16 women can do a piece of work in 5 days and  [#permalink]

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New post 24 Sep 2018, 11:27
Hi Mo2men,

You CAN use that same logic on that question, but it requires a bit more work than you did. I've posted an explanation in that thread.

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Re: If 12 men and 16 women can do a piece of work in 5 days and  [#permalink]

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New post 25 Sep 2018, 09:17
smcgrath12 wrote:
If 12 men and 16 women can do a piece of work in 5 days and 13 men and 24 women can do it in 4 days, how long will 7 men and 10 women take to do it?

(A) 4.2 days
(B) 6.8 days
(C) 8.3 days
(D) 9.8 days
(E) 10.2 days



hey everyone :) took me a while to find a shortcut to this problem :-)
Cheers,
D :)
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Re: If 12 men and 16 women can do a piece of work in 5 days and &nbs [#permalink] 25 Sep 2018, 09:17

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