From the list 6, 9, 15, 21, 24, 28, 30, which number is the odd one out based on divisibility by 3?

Introduction / Context:
This is another odd man out question that is based on a simple divisibility property. Most of the numbers in the list share a common feature related to divisibility by 3, and one number does not have this property. The question is designed to test your ability to quickly identify multiples of 3 by using a basic divisibility rule.

Given Data / Assumptions:

• The numbers given are 6, 9, 15, 21, 24, 28, and 30.
• We must pick the one number that does not share the key property common to the others.
• All numbers are positive integers.

Concept / Approach:
Use the divisibility rule for 3: a number is divisible by 3 if the sum of its digits is a multiple of 3. For example, 24 has digit sum 2 + 4 = 6, which is divisible by 3, so 24 is a multiple of 3. Apply this rule to each number in the list to see which one fails to be divisible by 3. That number will be the odd man out based on this property.

Step-by-Step Solution:
Check 6: 6 divided by 3 is 2, so 6 is divisible by 3. Check 9: 9 divided by 3 is 3, so 9 is divisible by 3. Check 15: 1 + 5 = 6, and 6 is divisible by 3, so 15 is divisible by 3. Check 21: 2 + 1 = 3, and 3 is divisible by 3, so 21 is divisible by 3. Check 24: 2 + 4 = 6, and 6 is divisible by 3, so 24 is divisible by 3. Check 30: 3 + 0 = 3, and 3 is divisible by 3, so 30 is divisible by 3. Check 28: 2 + 8 = 10, and 10 is not divisible by 3, so 28 is not divisible by 3. Therefore, 28 is the only number in the list that is not a multiple of 3 and is the odd man out.

Verification / Alternative Check:
We can also check by straightforward division. 6 / 3 = 2, 9 / 3 = 3, 15 / 3 = 5, 21 / 3 = 7, 24 / 3 = 8, and 30 / 3 = 10, all of which are integers. However, 28 divided by 3 gives 9 with a remainder of 1, clearly showing that 28 is not divisible by 3. Since every other number on the list divides evenly by 3, this confirms that 28 is the unique exception.

Why Other Options Are Wrong:

• Option 21: This is a multiple of 3 and shares the same divisibility property as the majority of the list.
• Option 24: Also a multiple of 3 and cannot be the odd one out based on this property.
• Option 30: Clearly divisible by 3, so it is not different in the required sense.
• Option 15: Another classic multiple of 3, with digit sum equal to 6.

Common Pitfalls:
A common mistake is to look for more complicated patterns such as prime numbers or differences between terms, instead of noticing the simple and strong property of being a multiple of 3. Another pitfall is to perform division mentally and make a small arithmetic slip, especially with larger numbers like 28 and 30. Using the digit sum rule for divisibility by 3 is usually faster and more reliable in such scenarios.

Final Answer:
The odd man out in the list, based on divisibility by 3, is 28.