In this numerical reasoning question on prime numbers, select the odd number from the following alternatives: 17, 23, 29 and 33.

Introduction / Context:
Odd one out questions involving numbers frequently use the concept of prime and composite numbers. In this problem, four numbers are given and you are asked to identify which one does not share the same property as the others. Recognising prime numbers quickly is an important skill for aptitude tests and forms the core idea tested here.

Given Data / Assumptions:

• The numbers given are 17, 23, 29 and 33.
• We use the standard definition of a prime number: a number greater than 1 that has exactly two distinct positive divisors, namely 1 and itself.
• We need to select the number that is not prime if the others are prime, or vice versa.

Concept / Approach:
The typical strategy is to test each number for divisibility by small primes such as 2, 3, 5 and 7. If a number has no divisors other than 1 and itself, it is prime. If it has more divisors, it is composite. When three numbers turn out to be primes and one is composite, the composite number becomes the odd one out in the group.

Step-by-Step Solution:
Step 1: Check 17. It is not divisible by 2, 3 or 5. The only divisors are 1 and 17, so 17 is prime. Step 2: Check 23. It is not divisible by 2, 3 or 5. The only divisors are 1 and 23, so 23 is also prime. Step 3: Check 29. It is not divisible by 2, 3 or 5. The only divisors are 1 and 29, so 29 is prime as well. Step 4: Check 33. It is divisible by 3, because 3 * 11 = 33. Therefore 33 has more than two divisors and is a composite number, not a prime number. Step 5: Hence 17, 23 and 29 are primes, while 33 is composite. So 33 is the odd one out.

Verification / Alternative check:
An alternative check is to use the digit sum method for divisibility by 3. For 33, the sum of digits is 3 + 3 = 6, which is divisible by 3, so 33 is divisible by 3. For 17, 23 and 29, the digit sums are 8, 5 and 11 respectively, none of which are divisible by 3. This confirms that 33 alone is composite and clearly different in nature from the other three numbers.

Why Other Options Are Wrong:
17 is wrong as the odd one out because it is a prime number, sharing the same property as 23 and 29. 23 is wrong as the odd one out because it is also prime and behaves like 17 and 29. 29 is wrong as the odd one out because it is prime and not uniquely different in this list.

Common Pitfalls:
One common mistake is to rely only on familiarity and assume that all two digit numbers ending with 3 or 7 are automatically prime. While many are, each number should still be checked for divisibility. Another pitfall is ignoring simple divisibility rules, such as the rule for 3, which makes identifying 33 as composite very quick. Carefully applying basic rules avoids such errors in timed exams.

Final Answer:
The only composite number among the given options, and therefore the odd one out, is 33.