If a, b, and c are three consecutive odd integers such that 10 < a < b < c < 20 and if b and c are prime numbers, what is the value of a + b?

Question: If a, b, and c are three consecutive odd integers such that 10 < a < b < c < 20 and if b and c are prime numbers, what is the value of a + b?

Solution:
Consecutive odd integers between 10 and 20 are 11,13,15,17,19
b and c are prime numbers.
Since a is at least 11, then b and c must be 17 and 19.

Hence a = 15, b = 17, c = 19.
∴ a + b = 32