In the following question, select the odd number from the given alternatives: 341, 342, 810 and 405. Three of these numbers are divisible by 9, while one of them is not divisible by 9. Based on this divisibility property, which number is the odd one out?

Introduction / Context:
This question is an odd one out problem based on divisibility rules. You are given four numbers and must determine which one does not share the same divisibility property as the others. Specifically, three of the numbers are divisible by 9, while one is not. Such questions are common in aptitude tests and help reinforce knowledge of divisibility rules.

Given Data / Assumptions:

• Numbers: 341, 342, 810, 405.
• We will apply the divisibility rule for 9.
• According to this rule, a number is divisible by 9 if the sum of its digits is divisible by 9.
• Three numbers are expected to satisfy this rule, while one will not.

Concept / Approach:
The divisibility rule for 9 is:

• Add the digits of the number.
• If the total is a multiple of 9 (9, 18, 27, and so on), the number is divisible by 9.

Using this, we will find which numbers are divisible by 9 and then identify the one that is not.

Step-by-Step Solution:
Step 1: Check 342. Sum of digits = 3 + 4 + 2 = 9. Since 9 is a multiple of 9, 342 is divisible by 9. Step 2: Check 810. Sum of digits = 8 + 1 + 0 = 9. Again, 9 is a multiple of 9, so 810 is divisible by 9. Step 3: Check 405. Sum of digits = 4 + 0 + 5 = 9. The sum is 9, so 405 is also divisible by 9. Step 4: Check 341. Sum of digits = 3 + 4 + 1 = 8. The sum 8 is not a multiple of 9, so 341 is not divisible by 9. Step 5: Therefore, 342, 810 and 405 are divisible by 9, but 341 is not. Hence, 341 is the odd one out.

Verification / Alternative check:
You can verify divisibility by actual division: 342 / 9 = 38, an integer. 810 / 9 = 90, an integer. 405 / 9 = 45, an integer. 341 / 9 is not an integer, as 9 * 37 = 333 and 9 * 38 = 342, so 341 lies between these two multiples. This confirms that only 341 fails the divisibility by 9 test.

Why Other Options Are Wrong:
342 is not odd because it passes the divisibility by 9 rule and is exactly divisible by 9. 810 is not odd because it is also exactly divisible by 9. 405 is not odd because it too is divisible by 9. 341 is the only number not divisible by 9, so it stands out from the rest.

Common Pitfalls:
A common pitfall is to forget or misapply the divisibility rule and instead rely on approximate division or guesswork. Another mistake is to confuse the rule for 3 with the rule for 9. While both involve digit sums, only sums that are multiples of 9 guarantee divisibility by 9. Careful addition and checking of the final sum avoids these errors.

Final Answer:
The number that is not divisible by 9 and is therefore the odd one out is 341.