Next number of the pattern 5 : 124 : : 7 : ? will be

Concept: This is a number-based analogy: the two terms in each pair are connected by the SAME arithmetic transformation. First discover the single rule that turns the first number into the second using the given pair, then apply that identical rule to the new number to find its counterpart.

Working:

1. Test the first pair (5 and 124) by cubing the first number: 5³ = 125.

2. Compare 125 with 124: 125 − 1 = 124, so the rule is "cube the number, then subtract 1."

3. Apply the same rule to 7: 7³ = 343.

4. Subtract 1: 343 − 1 = 342.

Cross-check: 124 is exactly 1 less than the perfect cube 125; 342 is exactly 1 less than the perfect cube 343 — the same offset-by-one relationship holds in both pairs, confirming the rule.

So 5 : 124 :: 7 : 342.