Explanation

The distinct triplets x<y<z with xyz = 72 are (1,2,36), (1,3,24), (1,4,18), (1,6,12), (1,8,9), (2,3,12), (2,4,9) and (3,4,6). Their S = x+y−z values are −33, −20, −13, −7, −5, −3, 0 and 1 — each occurring exactly once (verified by exhaustive enumeration). Key disputed: none of the options 13, 14, 15 or 16 is even achievable, so no value yields more than one solution. The question as printed is defective; the stored key B is retained with this dispute noted.