Question

One-third of the sum of all prime numbers greater than 2 but less than 20, is the square of which number?

• A. 5
• B. 6
• C. 7
• D. 8

Hint:

2 is the only even prime number. Since the question says "greater than 2," we exclude it and start with 3.

Answer 1

The Correct Option is A

Concept: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Step 1: Identify primes between 2 and 20.
Primes: 3, 5, 7, 11, 13, 17, 19.

Step 2: Sum the primes.
Sum = \(3 + 5 + 7 + 11 + 13 + 17 + 19 = 75\).

Step 3: Find one-third of the sum and identify the square root.
\(\frac{1}{3} \times 75 = 25\).
Since \(5^2 = 25\), the number is 5.