For median of {4,10,12,X} to equal median of {8,10,11,15} it would have to be 10.5; which is found by the following method:
As, number of elements are 4 (even number), we apply the median of even number of observations formula : {(n/2)th term + [(n/2)+1]th term}/2
From that we get, (2nd term + 3rd term) / 2 = (10+11) / 2 = 10.5
Hence, the only way median of {4,10,12,X} would match the above number would be if X was 11, then during ascending arrangement of elements for calculating median, it would be placed before 12 (at 3rd position); and median of {4,10,12,X} will be based on its 2nd and 3rd elements which would then be 10 and 11.
Hence, as X=11 which is > 10.5, the answer will be A) Quantity A is greater.