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

We can PLUG IN THE ANSWERS, which represent how many times a man's output exceeds that of a woman.

When the correct answer is plugged in, 3 men will take 5 fewer days to complete the job than 9 women.

B: 4

Let the rate for each woman = 1 unit per day and the rate for each man = 4 units per day.

Since it takes 6 days for 3 women and 2 men to complete the job, the job = (rate for 3 women and 2 men)(6 days) = (3*1 + 2*4)(6) = 66 units.

Time for 9 women to complete the job = \(\frac{work}{rate-for-9-women} = \frac{66}{(9*1)} = \frac{22}{3} ≈ 7\) days.

Time for 3 men to complete the job = \(\frac{work}{rate-for-3-men} = \frac{66}{(3*4)} = \frac{66}{12} = \frac{11}{2} ≈ 5\) days.

Doesn't work:

Here, 3 men take only about 2 fewer days than 9 women.

Eliminate B.

For 3 men to take 5 fewer days, the rate for each man must INCREASE.

Eliminate A.

D: 6

Let the rate for each woman = 1 unit per day and the rate for each man = 6 units per day.

Since it takes 6 days for 3 women and 2 men to complete the job, the job = (rate for 3 women and 2 men)(6 days) = (3*1 + 2*6)(6) = 90 units.

Time for 9 women to complete the job = \(\frac{work}{rate-for-9-women} = \frac{90}{(9*1)} = \frac{90}{9} = 10\) days.

Time for 3 men to complete the job = \(\frac{work}{rate-for-3-men} = \frac{90}{(3*6)} = \frac{90}{18} = 5\) days.

Success!

Here, 3 men take 5 fewer days than 9 women.

_________________

GMAT and GRE Tutor

Over 1800 followers

Click here to learn more

GMATGuruNY@gmail.com

New York, NY

If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.

Available for tutoring in NYC and long-distance.

For more information, please email me at GMATGuruNY@gmail.com.