Given Data

1. Analogy pair given: 6 : 37 :: 9 : ?

Question

Determine the missing number in the analogy.

Answer

82.

Solution

1. Analyze the transformation rule connecting 6 to 37:
2. 6^2 + 1 = 36 + 1 = 37.
3. Relationship rule: Second term = (First term)^2 + 1.
4. Apply the same rule to 9:
5. 9^2 + 1 = 81 + 1 = 82.
6. Therefore, the missing number is 82.