Let time taken by 'j' to type be 'j'.

We know that 1/m + 1/j = 1/12.5

i.e. 1/30 + 1/j = 1/12.5

i.e. (30+j)/30j = 1/12.5

i.e. 375 = 30j-12.5j=17.5j

i.e. j = 375/17.5=150/7

Let time taken by 'm' to edit be 'x' and that by 'j' be 'y'.

We know that 1/x + 1/y = 1/7.5

i.e. 1/x + 1/12 = 1/7.5

i.e. (12+x)/12x = 1/7.5

i.e. 90 = 12x-7.5x=4.5x

i.e. x = 90/4.5 = 20


Therefore answer = 150/7+20 = 41.4

Hi
I think the question should be re-written as a "which is the closest" or "approximately how long" question since 150/7 doesn't exactly equal 21.4... It's close to it: 21.42857...
There would never be an approximate right answer on the GMAT on a question which asks for a specific quantity

Well, this is how I figured a shorter solution:

M takes 30 hrs, two cons of equal cap take 12.5 *2 = 25 hrs each. Hence J will take less than 25 hrs (how much less --> guess above 20 at least?)
J takes 12 hrs, two cons of equal cap take 7.5 * 2 = 15 hrs each. Hence M will take more than 15 hrs (how much greater --> guess around 18)
Add them = GT20 + GT 15 = 35 . Only one option is above 35

Vaild question noburo: Here is the explanation->
J = 12, with same cap cons 1 = 15 and cons 2 = 15, Hence M needs to compensate for less hrs of J. at least 3 needs to be added to common hrs (assuming we are looking at Arithmetic mean)
M = 30, with same cap Cons 1 = 25 and Cons 2 = 25, , Hence J needs to compensate for more hrs of M. At lease 5 needs to be subtracted from common hrs (assuming we are looking at Arithmetic Mean)

We should also understand a bit about harmonic and arithmentic, a concept illustrated here: http://en.wikipedia.org/wiki/Harmonic_mean
Some points from the above post to consider:
For all positive data sets containing at least one pair of nonequal values, the harmonic mean is always the least of the three means, while the arithmetic mean is always the greatest of the three and the geometric mean is always in between
Since the harmonic mean of a list of numbers tends strongly toward the least elements of the list

In certain situations, especially many situations involving rates and ratios, the harmonic mean provides the truest average. For instance, if a vehicle travels a certain distance at a speed x (e.g. 60 kilometres per hour) and then the same distance again at a speed y (e.g. 40 kilometres per hour), then its average speed is the harmonic mean of x and y (48 kilometres per hour), and its total travel time is the same as if it had traveled the whole distance at that average speed

Hope this explains

Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, approximately how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

A. 41.4
B. 34.1
C. 13.4
D. 12.4
E. 10.8

Break down the problem into two pieces: typing and editing.

"Mary needs 30 hours to type the report" --> Mary's typing rate = 1/30 job/hour;
"Mary and Jim can type up a report in 12.5" and --> 1/30+1/x=1/12.5=2/25, where x is the time needed for Jim to type the report alone --> x=150/7;

"Jim needs 12 hours to edit the report" --> Jim's editing rate = 1/12 job/hour;
"Mary and Jim can edit a report in 7.5" and --> 1/y+1/12=1/7.5=2/15, where y is the time needed for Mary to edit the report alone --> y=20;

"How many hours will it take if Jim types the report and Mary edits it immediately after he is done" --> x+y=150/7+20=~41.4

Answer: A.
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Also, I don't believe this question is GMAT quality. It took me a few minutes to figure out what they were asking and that the two consultants were Mary and Jim since it wasn't stated. A correction is in order.
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kudos are appreciated

This is a very hard question, in part because it is not phrased particularly well. In particular, I believe the question wants us to understand that the "two consultant" mentioned in the first sentence are not two consultants in general, but rather, quite specifically, Mary & Jim.

Let's consider the typing rates.
Mary's rate = 1/30 (papers per hour)
Jim's rate = 1/X ----- where X = the hours it would take Jim to type one paper
Combined rate = 1/12.5 = 2/25
Big Idea: We can always add rates.
(Mary's rate) + (Jim's rate) = (combined rate)
(1/30) + (1/X) = 2/25
1/X = 2/25 - 1/30 = 12/150 - 5/150 = 7/150

X = 150/7 = 21 3/7

Now, let's consider the editing rates:
Mary's rate = 1/Y ------ where Y = the hours it would take Mary to edit one paper
Jim's rate = 1/12
Combined rate = 1/7.5 = 2/15
(Mary's rate) + (Jim's rate) = (combined rate)
1/Y + 1/12 = 2/15
1/Y = 2/15 - 1/12 = 8/60 - 5/60 = 3/60 = 1/20
Y = 20

Combined time = X + Y = 21 3/7 + 20 = 41 3/7 = 41.42857
Answer = A

Here's a related blog you may find helpful:
http://magoosh.com/gmat/2012/gmat-work-rate-questions/

Does all this make sense?

Mike
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Mike McGarry
Magoosh Test Prep

The question was not really difficult.....But lot of calculation involved...Can anyone suggest a shorter method