The work done by a man is double the work done by a woman in the same

Super easy. Convert 4 women into 2 men. 10 * 8 = 5 * x --> X= 16

There is no variable in the question, but there is some piece of information that would make our lives much easier.
The work done by a man is solving 2 GMAT questions in a day.
The work done by a woman is solving 1 GMAT question in a day.
10 men can solve 20 GMAT questions in a day.
10 men can solve 160 GMAT questions in a day. That's the job.
3 men can solve 6 GMAT questions in a day. 4 women can solve 4 GMAT questions in a day.
Together, 3 men and 4 women can solve 10 GMAT questions in a day.
It will take them 16 days to solve 160 GMAT questions.

Answer choice D.


ThatDudeKnowsHiddenPlugIn

Since a man can do double the work of a woman, one man is equivalent to two women. Thus, a group of 3 men and 4 women is equivalent to a group of 5 men. We are told that 10 men can do the work in 8 days and we need to find the number of days that 5 men can do the same work. Since the number of men is halved, the number of days will be doubled, which means that 5 men can do the work in 2 * 8 = 16 days.

Alternate Solution:

The rate of 10 men is \(\frac{1}{8}\frac{\text{job}}{\text{day}}\), which means the rate of one man is \(\frac{1}{80}\frac{\text{job}}{\text{day}}\).

We are told that one man can do double the work of a woman, which means that the rate of one man is double the rate of one woman. Thus, the rate of one woman is \(\frac{1}{160}\frac{\text{job}}{\text{day}}\). Then, the rate of 3 men and 4 women is:

\(\Rightarrow 3\times\frac{1}{80} + 4\times\frac{1}{160}\)
\(\Rightarrow \frac{3}{80} + \frac{2}{80}\)
\(\Rightarrow \frac{5}{80}\)
\(\Rightarrow \frac{1}{16}\)

Thus, the rate of 3 men and 4 women is \(\frac{1}{16}\frac{\text{job}}{\text{day}}\). This means that 3 men and 4 women can do \(\frac{1}{16}\) of the job in one day, so it will take 16 days to complete the whole job.

Answer: D