Classification – Odd one out (divisibility by 3) Three of the following integers are divisible by 3, while exactly one fails the divisibility-by-3 rule. Identify the number that is not divisible by 3 and mark it as the odd one out.

Introduction / Context:
Odd-one-out problems often revolve around a single arithmetic property that three options share while one does not. Here, that shared property is divisibility by 3. The quickest path to a reliable answer is to apply the digit-sum test, a standard technique taught in mental math and elementary number theory.

Given Data / Assumptions:

• Candidates: 63, 126, 215, 342
• Target property: divisibility by 3
• We assume ordinary base-10 integers with no hidden constraints.

Concept / Approach:
A number is divisible by 3 if and only if the sum of its digits is divisible by 3. This rule dramatically reduces calculation because we never need to perform long division; we only add digits and check membership in {0, 3, 6, 9, 12, 15, …}. When three items satisfy this rule and one item fails it, the failing item becomes the odd one out.

Step-by-Step Solution:
63 → 6 + 3 = 9 → divisible by 3 → fits pattern.126 → 1 + 2 + 6 = 9 → divisible by 3 → fits pattern.342 → 3 + 4 + 2 = 9 → divisible by 3 → fits pattern.215 → 2 + 1 + 5 = 8 → not divisible by 3 → breaks pattern.

Verification / Alternative check:
Direct division corroborates the test: 63/3 = 21, 126/3 = 42, 342/3 = 114, all integers; 215/3 = 71 remainder 2, not an integer. The two methods agree, so our classification is secure.

Why Other Options Are Wrong:

• 63: Clean multiple of 3; not the odd item.
• 126: Clean multiple of 3; not the odd item.
• 342: Clean multiple of 3; not the odd item.
• None of these: There is a unique non-multiple (215), so this distractor is incorrect.

Common Pitfalls:
Do not confuse “evenness” with divisibility by 3. Being even (like 342) gives no information about divisibility by 3. Also avoid mental shortcuts such as “numbers ending in 5 are divisible by 5 only”; although true about divisibility by 5, it says nothing about 3—always compute the digit sum. Finally, beware of assuming that the largest or smallest number is special; size is irrelevant here. The only decisive feature is the digit-sum rule, which uniquely flags 215 as the outlier.

Final Answer:
215