In this prime number classification question, you must select the odd number from the set: 71, 83, 89 and 93.

Introduction / Context:
This is an odd one out question based on prime and composite numbers. You are given four numbers and must identify which one does not belong to the same category as the others. Questions like this test your understanding of prime numbers and your ability to quickly check divisibility.

Given Data / Assumptions:

• The numbers in the options are 71, 83, 89 and 93.
• We suspect that three numbers might be prime, while one number is composite.
• Prime numbers are natural numbers greater than 1 that have exactly two distinct positive divisors: 1 and the number itself.
• Composite numbers have additional divisors other than 1 and themselves.

Concept / Approach:
To identify the odd number, we systematically test each option for primality by checking divisibility by small prime numbers like 2, 3, 5, 7 and 11. If a number is not divisible by any of these primes up to its approximate square root, it is prime. The number that turns out to be composite, while the others are prime, will be the odd one out.

Step-by-Step Solution:
Step 1: Check 71. It is odd and not divisible by 2. Sum of digits is 7 + 1 = 8, so it is not divisible by 3. It does not end in 0 or 5, so it is not divisible by 5. Dividing by 7 and 11 also does not yield an integer. Therefore, 71 is prime.Step 2: Check 83. It is odd and not divisible by 2. Sum of digits is 8 + 3 = 11, so not divisible by 3. It does not end in 5 or 0, so not divisible by 5. Basic checks with 7 and 11 show no exact division, so 83 is prime.Step 3: Check 89. It is odd and not divisible by 2. Sum of digits is 8 + 9 = 17, not a multiple of 3. It does not end in 5 or 0. Checks with 7 and 11 also fail to produce an integer quotient. Hence 89 is prime.Step 4: Check 93. It is odd but we must test divisibility by small primes. Sum of digits is 9 + 3 = 12, which is a multiple of 3. Therefore, 93 is divisible by 3, specifically 93 = 3 * 31, so it is composite.Step 5: Since 93 is composite and 71, 83, and 89 are prime, 93 is different from the others.

Verification / Alternative check:
We can quickly verify the result by noting that primes near 100 are often memorised, and 71, 83 and 89 are commonly known primes. Meanwhile, the clear divisibility of 93 by 3 confirms that it is not prime. This reinforces the conclusion that 93 is the only composite number in the list.

Why Other Options Are Wrong:
Option A, 71, is a prime number and therefore belongs to the same category as 83 and 89. Option B, 83, is also prime. Option C, 89, is another prime. The question asks for the number that is different from the others, so none of these can be the correct answer.

Common Pitfalls:
Some candidates may avoid checking divisibility carefully and guess based on the size or look of the number. Another mistake is to confuse near by composite numbers with primes. Practising basic divisibility tests for numbers up to 100 can greatly reduce such errors in the exam.

Final Answer:
The only composite number in the list is 93, so option D is correct.