Classification – Odd one out (perfect square among multiples of 11) Each number is a multiple of 11, but exactly one is also a perfect square. Identify the odd one out.

Introduction / Context:
Odd-one-out problems may combine two properties: a shared base property and an additional unique property for one element. Here, all values are multiples of 11; one stands apart by being a perfect square as well.

Given Data / Assumptions:

• Options: 22, 121, 242, 363
• Shared property: multiple of 11
• Distinctive property: perfect square

Concept / Approach:
Recognize 121 = 11 * 11 = 11^2, a perfect square. The others are 11 * 2 = 22, 11 * 22 = 242, 11 * 33 = 363, none of which are squares.

Step-by-Step Solution:
Factor 22 → 11 * 2 → not a square.Factor 121 → 11 * 11 → perfect square.Factor 242 → 11 * 22 → not a square.Factor 363 → 11 * 33 → not a square.

Verification / Alternative check:
Square test: nearest squares 10^2=100, 11^2=121, 12^2=144. Only 121 hits a perfect square exactly.

Why Other Options Are Wrong:

• 22: Multiple of 11 but not a square.
• 242: Multiple of 11 but not a square.
• 363: Multiple of 11 but not a square.
• None of these: There is exactly one standout (121).

Common Pitfalls:
Confusing “multiple of 11” with “power of 11.” Only equal factor pairs (k * k) produce perfect squares. 121 alone satisfies this.

Final Answer:
121