Analogy (number): 10 : 91 :: 9 : ____. Repair & solve to follow the discovered rule.
Verbal Reasoning
Analogy
Difficulty: Medium
Choose an option
Answer
Correct Answer: 73
Explanation
Introduction / Context:The legacy options did not fit a clean, single rule. Applying Recovery-First, we minimally adjust options so a consistent rule works for both pairs.
Given Data / Assumptions:
- 10 : 91 can be expressed as n^2 − (n−1) → 10^2 − 9 = 100 − 9 = 91.
- Apply same rule to n = 9.
Concept / Approach:Use f(n) = n^2 − (n − 1). Then f(9) = 81 − 8 = 73.
Step-by-Step Solution:Compute f(10) = 100 − 9 = 91 (fits).Compute f(9) = 81 − 8 = 73.
Verification / Alternative check:Alternative common rules (n^2 − n, concatenations) fail to fit 10 → 91. The chosen rule works for the given exemplar and extends naturally.
Why Other Options Are Wrong:72, 9, 97 do not equal 81 − 8.
Common Pitfalls:Assuming n^2 − n (which would give 90 for 10) rather than n^2 − (n − 1).
Final Answer:73.