In this divisibility based odd one out question, select the number that is not divisible by 3 among 462, 297, 674 and 891.

Introduction / Context:
This question is from the number system and divisibility chapter. You must decide which of the four given numbers is not a multiple of 3. Divisibility by 3 can be checked quickly using the digit sum rule, making this a classic and important pattern used in many aptitude tests.

Given Data / Assumptions:

• The numbers are 462, 297, 674 and 891.
• We use the standard divisibility rule for 3: a number is divisible by 3 if the sum of its digits is divisible by 3.
• The odd one out will be the only number whose digit sum is not divisible by 3.

Concept / Approach:
Instead of dividing each number by 3, we apply the digit sum test. We add the digits of each number and see whether the result is a multiple of 3. If three numbers pass this test and one fails, the failing number is the odd one out.

Step-by-Step Solution:
Step 1: For 462, digits are 4, 6 and 2. Sum = 4 + 6 + 2 = 12. Since 12 is divisible by 3, 462 is divisible by 3.Step 2: For 297, digits are 2, 9 and 7. Sum = 2 + 9 + 7 = 18. Since 18 is divisible by 3, 297 is divisible by 3.Step 3: For 891, digits are 8, 9 and 1. Sum = 8 + 9 + 1 = 18. Since 18 is divisible by 3, 891 is divisible by 3.Step 4: For 674, digits are 6, 7 and 4. Sum = 6 + 7 + 4 = 17. Since 17 is not divisible by 3, 674 is not divisible by 3.Step 5: Since 462, 297 and 891 are divisible by 3 and 674 is not, 674 is the odd one out.
Verification / Alternative check:
If you prefer direct division, you can compute 462 / 3 = 154, 297 / 3 = 99 and 891 / 3 = 297, all integers. For 674 / 3, you get approximately 224.67, which is not an integer. This numerical check matches the conclusion from the digit sum method and confirms that 674 is not a multiple of 3.

Why Other Options Are Wrong:
462 is not the odd one out because it is clearly a multiple of 3.
297 is also divisible by 3 and therefore belongs with 462 and 891.
891 is divisible by 3, so it also follows the common pattern and is not unique.

Common Pitfalls:
A common pitfall is misadding digits under exam pressure, which can lead to an incorrect conclusion about divisibility. Another mistake is to rely solely on the fact that a number is even or ends in certain digits, which is not relevant to divisibility by 3. Practicing the digit sum rule carefully and double checking simple additions can prevent these errors.

Final Answer:
The only number not divisible by 3 is 674, so 674 is the odd one out.