Three prime numbers p, q and r, each less than 20, are such that p − q = q − r. How many distinct possible values can we get for…

Question

Three prime numbers p, q and r, each less than 20, are such that p − q = q − r. How many distinct possible values can we get for (p + q + r)?

1. A. 4
2. B. 5
3. C. 6
4. D. More than 6 (Correct answer)

Correct Answer

Option D — More than 6

Detailed Solution & Explanation

The correct answer is More than 6.

Key Points

• Three primes p > q > r each < 20 in arithmetic progression (p−q = q−r).
• AP prime triplets: (3,5,7), (5,11,17), (7,11,15-not prime), (5,7,9-not prime), (3,7,11), (7,13,19), (3,11,19), (5,13,21-not prime), (11,13,17), (3,5,7),(13,11,9-no).
• Valid triplets give sums: 15, 33, 21, 39, 27, 33, 41. More than 6 distinct values are possible. Answer: More than 6.