LGOdream wrote:

Mary and Nancy can each perform a certain task in m and n hours, respectively. Is m<n?

(1) Twice the time it would take both Mary and Nancy to perform the task together, each working at their respective constant rates, is greater than m.

(2) Twice the time it would take both Mary and Nancy to perform the task together, each working at their respective constant rates, is less than n.

D it is.

The basic equation for RTD problems is work = rate X time

Let work be 1, so the rate by which Mary works per hour is 1/m

Similarly, the rate by which Nancy works per hour is 1/n

Statement 1:

With the information given in the question and using the RTD formula, the combined time to complete the same work (say 1) can be calculated as:

1= (1/m+1/n)t (t is the time)

Therefore, t = mn/(m+n)

Now, according to the statement, 2mn/(m+n) > m

Here we need to understand that m can not be negative. So we can divide both sides of the equation by m. By solving the equation we get,

n>m

Hence Sufficient.

Statement 2:

We can prove the statement to be true as Statement 1.

Hence Sufficient

Both statements are sufficient, so the answer is D.

_________________

If my post did a dance in your mind, send me the steps through kudos :)

My MBA journey at http://mbadilemma.wordpress.com/