Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on the shelf K. What is the median weight of 89 boxes on these shelves?

1) The heaviest box on shelf J weighs 15 pounds.
2) The lightest box on shelf K weighs 20 pounds.

Target question: What is the median weight of 89 boxes on these shelves?

Given: Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on the shelf K.
Let J1 be the weight of the lightest box on shelf J.
Let J2 be the weight of the 2nd lightest box on shelf J.
.
.
.
Let J45 be the weight of the heaviest box on shelf J.
Let K1 be the weight of the lightest box on shelf K.
Let K2 be the weight of the 2nd lightest box on shelf K.
etc.

So, the given information tells us that J1 < J2 < J3 < ... < J45 < K1 < K2 < ...< K44
Since the 89 boxes are now arranged in ascending order (according to weight), the median weight will be the weight of the middle box.
That is, the median weight, will be the weight of the 45th box.
So, we can REPHRASE the target question....
REPHRASED target question: What is the weight of box J45?

Statement 1: The heaviest box on shelf J weighs 15 pounds.
PERFECT! Box J45 is the heaviest box on shelf J
So, box J45 weighs 15 pounds.
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: The lightest box on shelf K weighs 20 pounds.
This tells us that box K1 weighs 20 pounds.
This does not help us find the weight of box J45
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent