In this divisibility based odd one out question, select the number that is not divisible by 4 among 156, 200, 182 and 240.

Introduction / Context:
This question tests divisibility skills in the number system segment. You must determine which of the four given numbers is not a multiple of 4. Divisibility by 4 is a basic concept frequently used in aptitude exams, and knowing the rule allows quick elimination of options.

Given Data / Assumptions:

• The numbers are 156, 200, 182 and 240.
• We assume the standard divisibility rule for 4: a number is divisible by 4 if the last two digits form a number divisible by 4.
• The odd one out will be the only number that fails this divisibility test.

Concept / Approach:
The key rule is that for any integer, if the number formed by its last two digits is divisible by 4, then the whole number is divisible by 4. Instead of dividing each number entirely, we only need to check the last two digits. By applying this rule, we can quickly find which number is not divisible by 4.

Step-by-Step Solution:
Step 1: For 156, look at the last two digits, 56. 56 / 4 = 14, an integer, so 156 is divisible by 4.Step 2: For 200, the last two digits are 00. 0 is divisible by 4, so 200 is divisible by 4.Step 3: For 240, the last two digits are 40. 40 / 4 = 10, an integer, so 240 is divisible by 4.Step 4: For 182, the last two digits are 82. 82 / 4 = 20.5, which is not an integer, so 182 is not divisible by 4.Step 5: Since 156, 200 and 240 are divisible by 4 and 182 is not, 182 is the odd one out.
Verification / Alternative check:
As an alternative check, you can perform direct division: 156 / 4 = 39, 200 / 4 = 50 and 240 / 4 = 60, all integers. For 182 / 4, you obtain 45.5, which is not an integer, confirming that 182 is not a multiple of 4. This reinforces the result obtained using the last two digits rule.

Why Other Options Are Wrong:
156 is not the odd one out as it is clearly divisible by 4 according to the rule.
200 is also divisible by 4 and therefore belongs with 156 and 240.
240 is divisible by 4 and fits the same pattern as 156 and 200.

Common Pitfalls:
A common mistake is to check only whether a number is even and assume that every even number is divisible by 4. This is incorrect, because many even numbers like 182 are not multiples of 4. Another error is to perform full division under time pressure and make arithmetic mistakes. Using the last two digits rule is both faster and more reliable in exam situations.

Final Answer:
The only number that is not divisible by 4 is 182, so 182 is the odd one out.