Among the numbers 708, 392, 618 and 816, which one is the odd one out?

Introduction / Context: This problem is a classic odd one out question. You are given four numbers and must identify which number does not share a common property that the other three have. Such questions improve your ability to spot hidden numerical properties quickly, such as divisibility rules or digit sum patterns.

Given Data / Assumptions: - The numbers are 708, 392, 618 and 816. - Exactly one number is different from the others with respect to a simple property. - The property is expected to be something standard like divisibility by a small integer.

Concept / Approach: A very efficient method with such problems is to test divisibility rules, especially divisibility by 2, 3, 5, 9 or 11. Here, all numbers are clearly even, so divisibility by 2 does not separate them. Next, checking divisibility by 3 can be done very fast using the rule that a number is divisible by 3 if the sum of its digits is divisible by 3.

Step-by-Step Solution: Step 1: Check divisibility by 3 using digit sums. For 708: digit sum is 7 + 0 + 8 = 15, which is divisible by 3. For 392: digit sum is 3 + 9 + 2 = 14, which is not divisible by 3. For 618: digit sum is 6 + 1 + 8 = 15, which is divisible by 3. For 816: digit sum is 8 + 1 + 6 = 15, which is divisible by 3. Step 2: Compare the properties. 708, 618 and 816 are all divisible by 3. 392 alone is not divisible by 3. Therefore, 392 is the odd one out.

Verification / Alternative check: As an additional check, divide the numbers directly by 3: 708 / 3 = 236, 618 / 3 = 206, and 816 / 3 = 272 are all integers. However, 392 / 3 gives a non integer value. This confirms the earlier conclusion based on digit sum.

Why Other Options Are Wrong: Option A (708) is divisible by 3, so it shares the key property with 618 and 816. Option C (618) is also divisible by 3 and cannot be the odd one out. Option D (816) again is divisible by 3 and fits the group pattern. Option B (392) alone fails the divisibility by 3 test, so it is the correct odd one out.

Common Pitfalls: Some students may try to factorise all four numbers fully, which is time consuming. Others might look for more complicated patterns such as prime factors when a simple divisibility rule is sufficient. Remember that aptitude tests favour quick recognition using simple rules. Always check basic divisibility by 2, 3, 5, 9 before moving to complex reasoning.

Final Answer: The odd one out is 392.