In the following question, four three digit numbers are given. In three of these numbers, the value is a multiple of 12, while one number is not a multiple of 12. Select the number which is not divisible by 12 (odd number out).

Introduction / Context:
This numerical reasoning question focuses on identifying multiples of 12. You are given several three digit numbers and must find which one is not divisible by 12. Such questions improve your familiarity with divisibility tests and common multiples and are often seen in quantitative aptitude sections.

Given Data / Assumptions:
- The options are 308, 108, 288, 240, and 156.
- A number is divisible by 12 if it is divisible by both 3 and 4, since 12 = 3 * 4.
- In most options, the numbers are clean multiples of 12.
- Exactly one number is not a multiple of 12 and must be selected as the odd one out.

Concept / Approach:
The efficient way to approach this is to use divisibility rules for 3 and 4. A number is divisible by 3 if its digit sum is divisible by 3. A number is divisible by 4 if the last two digits form a number that is divisible by 4. If both conditions hold, the number is divisible by 12. Applying these checks to each option is much faster than performing full division for all numbers.

Step-by-Step Solution:
Step 1: Check 108. Digit sum is 1 + 0 + 8 = 9, divisible by 3. Last two digits 08 form 8, which is divisible by 4. So 108 is divisible by 12.Step 2: Check 288. Digit sum is 2 + 8 + 8 = 18, divisible by 3. Last two digits 88 give 88, which is divisible by 4 (since 4 * 22 = 88). So 288 is a multiple of 12.Step 3: Check 240. Digit sum is 2 + 4 + 0 = 6, divisible by 3. Last two digits 40 form 40, which is divisible by 4. So 240 is also a multiple of 12.Step 4: Check 156. Digit sum is 1 + 5 + 6 = 12, divisible by 3. Last two digits 56 form 56, which is divisible by 4. So 156 is a multiple of 12.Step 5: Check 308. Digit sum is 3 + 0 + 8 = 11, which is not divisible by 3, so 308 is not divisible by 3.Step 6: Since 308 fails the divisibility by 3 test, it cannot be divisible by 12, and therefore it is the only non multiple of 12 in the list.

Verification / Alternative check:
As a verification, you can perform quick mental division. 108, 288, 240, and 156 are all familiar multiples of 12 from tables, such as 12 * 9 = 108 and 12 * 13 = 156. For 308, trying 12 * 25 = 300 and 12 * 26 = 312 shows that 308 is between these multiples and not equal to any. Thus, 308 is not divisible by 12, confirming our result from the divisibility rule method.

Why Other Options Are Wrong:
108, 288, 240, and 156 all pass both divisibility tests for 3 and 4 and are therefore multiples of 12. Because they share the same property, they form one consistent group. None of them can be considered the odd one out when compared with 308, which clearly fails the 12 multiple criteria.

Common Pitfalls:
Students often forget that 12 requires divisibility by both 3 and 4, not just one of them. Another common error is to miscalculate digit sums or to check only one of the conditions. By systematically applying both tests and double checking arithmetic, you can avoid these mistakes and handle similar questions with confidence.

Final Answer:
308