In the number series 720, 732, 708, 742, 696, which one is the odd man out based on divisibility by 12?

Introduction / Context:
This problem presents the series 720, 732, 708, 742, 696 and asks you to find the odd man out. The numbers are all in a similar range, so a sensible approach is to check simple divisibility properties, especially by numbers like 3, 4 or 12 that are common in aptitude tests.

Given Data / Assumptions:
The terms given are:

• 720
• 732
• 708
• 742
• 696

We assume that most of these numbers share a straightforward divisibility property, while one number fails this test and therefore stands out as the odd one.

Concept / Approach:
A good candidate to test here is divisibility by 12, which requires that a number be divisible both by 3 and by 4. The test for divisibility by 3 uses the sum of digits, and the test for divisibility by 4 uses the last two digits. If four of the numbers are multiples of 12 and one is not, the non multiple identifies the odd one out.

Step-by-Step Solution:
Step 1: Check 720. The sum of digits is 7 + 2 + 0 = 9, which is divisible by 3. The last two digits 20 give 20 / 4 = 5, so 720 is divisible by 4. Therefore, 720 is divisible by 12.Step 2: Check 732. The sum of digits is 7 + 3 + 2 = 12, divisible by 3, and 32 / 4 = 8, so 732 is divisible by 4, hence by 12.Step 3: Check 708. The sum of digits is 7 + 0 + 8 = 15, divisible by 3, and 8 / 4 = 2, so 708 is divisible by 4 and therefore by 12.Step 4: Check 696. The sum of digits is 6 + 9 + 6 = 21, divisible by 3, and 96 / 4 = 24, so 696 is divisible by 4 and thus by 12.Step 5: Check 742. The sum of digits is 7 + 4 + 2 = 13, which is not divisible by 3, so 742 fails the divisibility by 3 test and therefore cannot be divisible by 12.

Verification / Alternative check:
We can also divide each number directly by 12: 720 / 12 = 60, 732 / 12 = 61, 708 / 12 = 59, 696 / 12 = 58, all integers. But 742 / 12 is not an integer. This confirms that 742 is the only number that is not a multiple of 12, while all others are exact multiples of 12 with consecutive integer quotients 60, 61, 59 and 58.

Why Other Options Are Wrong:
The numbers 696, 708 and 732, as well as 720, all satisfy the divisibility by 12 condition. Removing any of them as the odd one out would leave a set where 742 is still not divisible by 12, which would be inconsistent. Hence, they cannot be correct choices for the odd term.

Common Pitfalls:
Some students may be tempted to look only at the approximate order or spacing of the numbers. However, there is no clear arithmetic or geometric sequence here. Instead, the question relies on a very standard divisibility rule, so checking divisibility by small integers is an effective and efficient strategy.

Final Answer:
The only number in the list that is not divisible by 12 is 742.