In this number-classification odd-man-out question, select the number that does not follow the same divisibility pattern as the others.

Introduction / Context:
This is a straightforward numerical odd-man-out question. Four two-digit numbers are given, and three of them share the property of being divisible by 3, while one does not. Recognising this divisibility pattern allows us to identify the odd number quickly, using the familiar rule for divisibility by 3.

Given Data / Assumptions:

• Numbers given: 24, 39, 65 and 51.
• We use basic divisibility rules taught in school mathematics.
• We seek a single property common to three numbers but absent in one.

Concept / Approach:
The key idea is the rule for divisibility by 3: a number is divisible by 3 if the sum of its digits is divisible by 3. We can apply this rule to each of the given numbers. If three numbers satisfy this rule and one does not, then the number that fails the test is the odd-man-out. This test is quick and avoids the need for full long division.

Step-by-Step Solution:
Step 1: Check 24. The digit sum is 2 + 4 = 6. Since 6 is divisible by 3, 24 is divisible by 3. Step 2: Check 39. The digit sum is 3 + 9 = 12. Since 12 is divisible by 3, 39 is divisible by 3. Step 3: Check 51. The digit sum is 5 + 1 = 6. Since 6 is divisible by 3, 51 is divisible by 3. Step 4: Check 65. The digit sum is 6 + 5 = 11. Since 11 is not divisible by 3, 65 is not divisible by 3. Step 5: Summarise results. 24, 39 and 51 are all multiples of 3, while 65 is not a multiple of 3. Step 6: Conclude that 65 is the odd number.

Verification / Alternative check:
We can further verify by performing division or factoring. 24 = 3 * 8, 39 = 3 * 13 and 51 = 3 * 17, clearly showing they are multiples of 3. Meanwhile, attempting 65 / 3 gives a non-integer value, confirming 65 is not divisible by 3. This supports our conclusion from the digit sum method. No other equally simple pattern gives a clean 3 versus 1 split among these numbers.

Why Other Options Are Wrong:
24 is not odd because it is divisible by 3 and belongs with 39 and 51. 39 is also a multiple of 3 and fits the same group. 51 is again divisible by 3, so it behaves just like the other two. Since these three share a clear divisibility property, they cannot be treated as odd. Only 65 fails to be divisible by 3, which makes it the odd-man-out.

Common Pitfalls:
Some students may focus on divisibility by 5 because 65 ends in 5, but that property does not distinguish 65 cleanly from the others. The number 24 is not divisible by 5, but neither are 39 and 51, so that does not create a 3 versus 1 grouping. The correct distinguishing feature is divisibility by 3. Therefore, always consider which divisibility rule gives a consistent pattern across most numbers before making a choice.

Final Answer:
The odd number is 65, because 24, 39 and 51 are all divisible by 3, while 65 is not a multiple of 3.