Square-minus-one pattern 10 → 99 implies n^2 − 1; find the analogous value for 9 → ?

Introduction / Context:This pattern uses a simple transformation based on squaring and subtracting one. Such forms are common in quick-reasoning tests.

Given Data / Assumptions:

• 10 maps to 99.
• We test f(n) = n^2 − 1.

Concept / Approach:Compute 10^2 − 1 = 100 − 1 = 99. The rule fits perfectly, so apply it to 9.

Step-by-Step Solution:For n = 9: 9^2 − 1 = 81 − 1 = 80.

Verification / Alternative check:Note that n^2 − 1 factors as (n − 1)(n + 1). For n=10, (9)(11)=99; for n=9, (8)(10)=80, confirming the result.

Why Other Options Are Wrong:69 and 97: Do not equal 9^2 − 1.49: Equals 7^2, unrelated to the rule.

Common Pitfalls:Using n^2 or n^2 + 1 instead of n^2 − 1; confusing the pattern with “multiply consecutive numbers”.

Final Answer:80