How many prime numbers lie between 0 and 50 (count all primes p with 2 ≤ p ≤ 49)?

Introduction / Context:Counting primes in a small interval checks quick recall of basic primes and composite recognition. The range 0 to 50 is common in aptitude tests and can be handled by enumeration or a mental sieve of Eratosthenes.

Given Data / Assumptions:

• We count primes with 2 ≤ p ≤ 49 (since “between 0 and 50” excludes 50).
• 1 is not prime.
• Eliminate multiples of 2, 3, 5, and 7 as composites where applicable.

Concept / Approach:List all primes under 50 and count them carefully, ensuring none are missed or misclassified.

Step-by-Step Solution:

Verification / Alternative check:Mental sieve: strike out even numbers > 2, multiples of 3, of 5, and of 7; the remaining list matches the primes above.

Why Other Options Are Wrong:13, 14, and 16 miscount by omitting or including numbers incorrectly; 12 is the count under 40, not under 50.

Common Pitfalls:Including 1 as prime or forgetting 41, 43, and 47.

Final Answer:15