Replace the question mark with the suitable option. 256 : 4086 :: ?

Concept: In a number-pair analogy, both numbers of each pair are linked by one fixed rule derived from a base value x. Once that rule is found from the given pair, the correct answer pair must satisfy the exact same rule using its own x value.

Steps:

1. 256 = 162 (16 squared = 256).

2. 4086 = 163 − 10 (16 cubed = 4096, and 4096 − 10 = 4086).

3. So the rule linking the pair is: first term = x2, second term = x3 − 10.

4. Testing 225 : 3365 → 225 = 152 and 153 − 10 = 3375 − 10 = 3365, which matches exactly.

Cross-check (other options):

• 144 : 3032 → 144 = 122, but 123 − 10 = 1718, not 3032, so this pair does not satisfy the rule.

• 132 : 3012 → 132 is not a perfect square, so it cannot satisfy the x2 part of the rule.

• 160 : 3600 → 160 is not a perfect square, so it cannot satisfy the x2 part of the rule.

Result: 225 : 3365 is the pair that continues the pattern.