Just for a start let us use two statements

m < 2mn/(m+n) < n.. Here we can see Option C is good for sure - so test for A/B/D

Now let us take only first part..

m < 2mn/(m+n) => m+n < 2n => n>m .. A is suff

Now let us take the second part

this also gives n > m .. B is also suff

D

Thanks for the quick reply.

How did you translate

Twice the time it would take Mary and Nacy to perform the task together, at their respective rate is greater than m to following:

m < 2mn/(m+n)

I was converting the statement as follows:

- Marry's Time =m (Her rate 1/m)
- Nancy's Time =n (Her rate 1/n)

Twice the time it would take both Mary and Nancy to perform the task together == 2(m+n)

is Greater than m = >m

==> 2(m+n) >m.

I know this is not right! I can see I need the rate part in the conversion, but it does not intuitively make sense. Can you describe the logic flow here, so I can tackle such problems following a clear logic.

iwillsurvive101 wrote:Mary and Nancy can perform a certain task in m and n hours respectively. Is m < n?

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

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

How would you guys solve this one?

Many DS rate problems can be solved quickly by REASONING our way to the correct answer.

Statement 1: Twice the time it would take Mary and Nancy to perform the task together, each working at their respective rates, is greater than m.
In other words, if we double the time needed by Mary and Nancy together, the result is MORE time than Mary needs to complete the task alone.
This means that Mary is working FASTER than Nancy.
Thus, Mary needs LESS TIME than Nancy to complete the task alone, and m<n.
SUFFICIENT.

Statement 2: Twice the time it would take Mary and Nancy to perform the task together, each working at their respective constant rates, is less than n.
In other words, if we double the time needed by Mary and Nancy together, the result is LESS time than Nancy needs to complete the task alone.
This means that Nancy is working MORE SLOWLY than Mary.
Thus, Nancy needs MORE TIME than Mary to complete the task alone, and n>m.
SUFFICIENT.

The correct answer is D.

iwillsurvive101 wrote:Thanks for the quick reply.

How did you translate

Twice the time it would take Mary and Nacy to perform the task together, at their respective rate is greater than m to following:

m < 2mn/(m+n)

I was converting the statement as follows:

- Marry's Time =m (Her rate 1/m)
- Nancy's Time =n (Her rate 1/n)

Twice the time it would take both Mary and Nancy to perform the task together == 2(m+n)

is Greater than m = >m

==> 2(m+n) >m.

I know this is not right! I can see I need the rate part in the conversion, but it does not intuitively make sense. Can you describe the logic flow here, so I can tackle such problems following a clear logic.

Below is an algebraic translation of each statement.

Statement 1: Twice the time for Mary and Nancy working together is greater than m.
Rate for Mary = 1/m.
Rate for Nancy = 1/n.
Combined rate for Mary and Nancy = 1/m + 1/n.

Time for Mary and Nancy working together = 1/(1/m + 1/n) = 1/ [(m+n)/mn] = mn/(m+n).
Twice the time for Mary and Nancy working together = 2mn/(m+n).

Since twice the time for Mary and Nancy working together is greater than m:
2mn/(m+n) > m.
2n/(m+n) > 1.
2n > m+n.
n > m.
SUFFICIENT.

Statement 2: Twice the time for Mary and Nancy working is less than n.
2mn/(m+n) < n.
2m/(m+n) < 1.
2m < m+n.
m < n.
SUFFICIENT.

These algebraic translations take time.
It's much quicker here to REASON our way to the correct answer.

[Deleted by GMATGuruNY -- accidental duplicate post]