Find the odd number from the following alternatives based on divisibility by 5.

Introduction / Context:
This odd one out question checks your understanding of divisibility by 5, a very common rule in arithmetic and number theory. Having these rules at your fingertips helps in speed based exams where quick elimination of options is essential.

Given Data / Assumptions:

• The four numbers provided are: 82, 75, 64, and 31.
• You are required to pick the number that does not behave like the others with respect to divisibility by 5.
• Use the standard rule that a number divisible by 5 ends in 0 or 5.

Concept / Approach:
The divisibility rule for 5 is straightforward. If the last digit (units digit) of a number is either 0 or 5, the number is divisible by 5. If the last digit is anything else, the number is not divisible by 5. Applying this rule to all four options lets you group them accordingly and identify the odd number based on which group is smaller.

Step-by-Step Solution:
Step 1: Look at 82. Its last digit is 2, so 82 is not divisible by 5. Step 2: Look at 64. Its last digit is 4, so 64 is not divisible by 5. Step 3: Look at 31. Its last digit is 1, so 31 is also not divisible by 5. Step 4: Look at 75. Its last digit is 5, so 75 is divisible by 5. Step 5: Three numbers are not divisible by 5, and only one number is divisible by 5, so the divisible number is the odd one out.

Verification / Alternative check:
You can verify this by actual division. Dividing 75 by 5 gives exactly 15, which is an integer. If you try 82 divided by 5, you get 16.4, which is not an integer. Similarly, 64 divided by 5 and 31 divided by 5 yield non integer results. This confirms that 75 is the only number divisible by 5 among the four options.

Why Other Options Are Wrong:

• 82: Ends with 2 and is not divisible by 5, similar to 64 and 31.
• 64: Ends with 4 and therefore does not satisfy the divisibility rule for 5.
• 31: Ends with 1 and also is not divisible by 5, so it follows the same pattern as 82 and 64.

Common Pitfalls:
A common mistake is to look for patterns like even or odd numbers and ignore the more relevant divisibility rule. Here, parity does not separate one number clearly from the others because there are both even and odd numbers in the options. Focusing on the last digit and recalling the rule for divisibility by 5 leads to a faster and more accurate solution.

Final Answer:
75