Select the related number from the given alternatives. ? : 65 :: 08 : 28

Concept

Concept: In a number analogy of the form A : B :: C : D, the two numbers inside each pair are linked by one and the same rule, and you must make the unknown pair obey exactly the rule you extract from the known pair. Here each pair is generated by a single counting index n, where the first number is A = n2 − 1 and the second number is B = n3 + 1.

Application

1. From the known pair 08 : 28, find n. The first number gives n2 − 1 = 8, so n2 = 9 and n = 3; the second number checks out as n3 + 1 = 33 + 1 = 27 + 1 = 28. So the known pair is the n = 3 case.

2. Apply the identical rule to the unknown pair ? : 65. The second number fixes n: n3 + 1 = 65, so n3 = 64 and n = 4.

3. Compute the missing first number with the same formula A = n2 − 1 for n = 4: A = 42 − 1 = 16 − 1 = 15.

Cross-check

Cross-check: with n = 4 the pair becomes 15 : 65, and 42 − 1 = 15 while 43 + 1 = 65, so both numbers come from the same index n = 4 — exactly mirroring how 08 : 28 both come from n = 3. The missing number is 15.