In this number classification question, select the odd number from the following alternatives: 75, 65, 82 and 85.

Introduction / Context:
This question checks your basic divisibility knowledge. You are given four numbers 75, 65, 82 and 85. Three of these numbers share a common divisibility property, while one number does not. In particular, three of them are multiples of 5, and one is not. You must determine which number does not follow the same divisibility rule and mark it as the odd one out.

Given Data / Assumptions:

• Numbers: 75, 65, 82 and 85.
• We focus on divisibility by 5, which is easy to test from the units digit.
• In valid numbers, the units digit should be 0 or 5.
• Exactly one number does not satisfy this condition.

Concept / Approach:
A number is divisible by 5 if and only if its last digit is 0 or 5. This rule allows very quick checking without long division. We simply inspect the units digit of each number in the list. If three numbers end in 5 or 0 and one number does not, that number becomes the odd one out, because it is not a multiple of 5.

Step-by-Step Solution:
Step 1: Check 75.The last digit of 75 is 5. Therefore, 75 is divisible by 5.Step 2: Check 65.The last digit of 65 is 5. So 65 is also divisible by 5.Step 3: Check 85.The last digit of 85 is 5 as well, making it another multiple of 5.Step 4: Check 82.The last digit of 82 is 2. A number ending in 2 is not divisible by 5. So 82 is not a multiple of 5.Step 5: Identify the odd number.Since 75, 65 and 85 are divisible by 5 and 82 is not, 82 is the odd number out.

Verification / Alternative check:
You can confirm this by performing quick divisions. 75 / 5 = 15, 65 / 5 = 13 and 85 / 5 = 17, all of which are exact integers. In contrast, 82 / 5 = 16.4, which is not an integer, so 82 is not divisible by 5. This alternative check supports the result you already obtained just by looking at the last digit, and highlights how divisibility rules help in fast reasoning.

Why Other Options Are Wrong:
75: Ends with 5 and is exactly divisible by 5, so it matches the main pattern.
65: Also ends with 5 and is a multiple of 5, so it belongs with 75 and 85.
85: Another number ending with 5 and therefore divisible by 5, not the odd one.

Common Pitfalls:
Some learners might overthink and start checking for prime or composite nature or divisibility by 3, when the simplest classification is based on divisibility by 5. In many basic odd one out questions, the examiner expects you to apply simple divisibility rules. Always scan for obvious properties like parity and divisibility by 5 or 10 before attempting more advanced analyses.

Final Answer:
The odd number is 82, because it is not divisible by 5, while 75, 65 and 85 are all multiples of 5.