Hi NandishSS,

This is a great 'concept' question, meaning that you don't really have to do any math to answer it as long as you understand the concepts involved.

We're told that EACH of the 45 boxes on shelf J weighs LESS than EACH of the 44 boxes on shelf K. We're asked for the MEDIAN weight of the 89 boxes.

To start, the 'median box' will be the 45th box. Since each of the boxes on shelf J weigh LESS than each of the boxes on shelf K, the 'heaviest' box on shelf J will be the median. If we have that one value, then we can answer the question.

1) The heaviest box on shelf J weighs 15 pounds.

This Fact gives us exactly what we need to answer the question.
Fact 1 is SUFFICIENT

2) The lightest box on shelf K weighs 20 pounds.

Unfortunately, this Fact doesn't tell us anything about the weights of the boxes on shelf J. Maybe the median is 19 pounds, but it could just as easily be 18 pounds, 17 pounds, 16.5 pounds, etc.
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich