Odd One Out — Among the quadruples [77, 70, 49, 56], [56, 64, 96, 48], [66, 44, 23, 60], [18, 27, 63, 81], select the one that does not consist of multiples of a single common base.

Introduction / Context:Grouping by a shared factor is a common pattern in set-classification problems. Three sets here are built from clean multiples of a single number; one set is not.

Given Data / Assumptions:

• [77, 70, 49, 56]: all multiples of 7.
• [56, 64, 96, 48]: all multiples of 8.
• [18, 27, 63, 81]: all multiples of 9.
• [66, 44, 23, 60]: 66 and 44 are multiples of 11; 60 is not; 23 is prime and not a multiple of 11.

Concept / Approach:For each set, check divisibility by a candidate base. A valid set will see all members divisible by that base.

Step-by-Step Solution:Divisible by 7? 77, 70, 49, 56 — all yes.Divisible by 8? 56, 64, 96, 48 — all yes.Divisible by 9? 18, 27, 63, 81 — all yes.Divisible by 11? 66 (yes), 44 (yes), 23 (no), 60 (no) — mixed.

Verification / Alternative check:Compute gcd of each set: gcd(77,70,49,56)=7; gcd(56,64,96,48)=8; gcd(18,27,63,81)=9; gcd(66,44,23,60)=1 → confirms the outlier set.

Why Other Options Are Wrong:

• [77, 70, 49, 56]: valid “all multiples of 7.”
• [56, 64, 96, 48]: valid “all multiples of 8.”
• [18, 27, 63, 81]: valid “all multiples of 9.”

Common Pitfalls:Picking a base that only fits some elements (e.g., “multiples of 2” would match many numbers across sets but not isolate a single outlier).

Final Answer:66, 44, 23, 60