Classification – Odd one out (divisibility by 6) Three of the given numbers are multiples of 6. Identify the number that is not divisible by 6 and mark it as the odd one out.

Introduction / Context:
A multiple of 6 must be divisible by both 2 and 3. This two-part criterion quickly separates qualifying values from look-alikes. In sets where three satisfy the rule, the lone non-qualifier becomes the odd element.

Given Data / Assumptions:

• Candidates: 6, 24, 64, 120
• We test the 2-and-3 divisibility condition for 6.

Concept / Approach:
Check evenness (divisible by 2) and the digit-sum test for 3. A number must pass both to be a multiple of 6.

Step-by-Step Solution:
6 → even and 6/3 = 2 → multiple of 6.24 → even; 2 + 4 = 6 → divisible by 3 → multiple of 6.120 → even; 1 + 2 + 0 = 3 → divisible by 3 → multiple of 6.64 → even; 6 + 4 = 10 → not divisible by 3 → not a multiple of 6.

Verification / Alternative check:
Direct division: 6/6 = 1, 24/6 = 4, 120/6 = 20 (integers). 64/6 = 10 remainder 4 → not an integer.

Why Other Options Are Wrong:

• 6: Multiple of 6.
• 24: Multiple of 6.
• 120: Multiple of 6.
• None of these: There is a unique non-multiple (64).

Common Pitfalls:
Assuming that any even number qualifies. Evenness alone is insufficient; the 3-divisibility condition must also hold.

Final Answer:
64