In this number classification question, select the odd number from the given alternatives based on prime and composite properties.

Introduction / Context:
This quantitative aptitude question asks you to identify the odd number based on basic number theory, especially the concept of prime and composite numbers. Recognizing whether a number has more than two factors is a fundamental skill that appears regularly in competitive exams. Here, four numbers are given, and one of them has a different factor property from the others.

Given Data / Assumptions:
- The options are 42, 84, 91, and 71.- All are two digit positive integers.- The question is likely based on whether the numbers are prime or composite.

Concept / Approach:
A prime number has exactly two distinct positive divisors, 1 and the number itself. A composite number has more than two divisors. To solve this question, you test each option for divisibility by small primes such as 2, 3, 5, 7, and 11. The number that remains with only two factors is prime and will be the odd one out if the others are composite.

Step-by-Step Solution:
Step 1: 42 is even, so divisible by 2. It is also divisible by 3 and 7. Hence, 42 is composite.Step 2: 84 is even and divisible by 2, 3, 4, 6, 7, and more. So 84 is composite.Step 3: 91 is divisible by 7 because 7 multiplied by 13 gives 91. So 91 is composite.Step 4: 71 is not divisible by 2, 3, 5, 7, or 11. It has no divisors other than 1 and 71.Step 5: Therefore, 71 is a prime number, whereas the other three are composite.

Verification / Alternative check:
To double check, you can try dividing 71 by all primes up to its square root. The square root of 71 is slightly more than 8, so you only need to test 2, 3, 5, and 7. None of these divide 71 evenly, confirming that 71 is prime.

Why Other Options Are Wrong:
42: Composite with many factors.84: Also composite with multiple divisors.91: Composite because it is 7 multiplied by 13.

Common Pitfalls:
A common mistake is to assume that any number ending with 1 is prime, which is not always true. Here, 91 ends with 1 but is composite. You should always check divisibility rather than rely only on endings.

Final Answer:
The odd number is 71 because it is prime, while the other three numbers are composite.