In the sequence 152, 124, 96, 69, 40, which number is the odd man out based on divisibility by 4?

Introduction / Context:
This odd-man-out question relies on a basic divisibility rule. You are asked to decide which number among 152, 124, 96, 69 and 40 does not share a simple divisibility property with the others. Such questions help reinforce quick mental checks about multiples of small integers like 2 and 4.

Given Data / Assumptions:
The given numbers are 152, 124, 96, 69 and 40. We assume that the relevant property involves divisibility by 4, which can be checked using the standard rule: a number is divisible by 4 if and only if its last two digits form a number that is divisible by 4.

Concept / Approach:
The most efficient strategy is to apply the divisibility-by-4 rule to each number. If four of them are divisible by 4 and one is not, the one that fails this test will be the odd man out. This avoids complex calculations and uses only the last two digits of each number.

Step-by-Step Solution:
Step 1: Check 152. The last two digits are 52. Since 52 / 4 = 13, 152 is divisible by 4.Step 2: Check 124. The last two digits are 24. Since 24 / 4 = 6, 124 is divisible by 4.Step 3: Check 96. The last two digits are 96. Since 96 / 4 = 24, 96 is divisible by 4.Step 4: Check 40. The last two digits are 40. Since 40 / 4 = 10, 40 is divisible by 4.Step 5: Check 69. The last two digits are 69. Since 69 / 4 is not an integer (it equals 17.25), 69 is not divisible by 4.Step 6: Therefore, 69 alone fails the divisibility-by-4 test and is the odd man out.

Verification / Alternative check:
We can also look at the even or odd nature of the numbers: 152, 124, 96 and 40 are all even, while 69 is odd. No odd number can be divisible by 4, so this immediately marks 69 as different. The more refined test using the last two digits confirms that all the other four numbers are exact multiples of 4, reinforcing our conclusion.

Why Other Options Are Wrong:
124, 96 and 40, as well as 152, are all divisible by 4 and therefore share a common property. Removing any of them as the odd one out would leave a group containing an odd number (69) that is not divisible by 4 together with numbers that are, which would make less sense from a classification viewpoint.

Common Pitfalls:
Some test-takers may focus only on whether numbers are even or odd and may not notice that all even numbers except 69 also share the richer property of being divisible by 4. While parity is a helpful first check, using the full divisibility rule allows you to justify your choice more strongly and confidently.

Final Answer:
The only number that is not divisible by 4 is 69, so it is the odd man out.