IMC 2012 Q7
7. The prime numbers \(p\) and \(q\) are the smallest primes that differ by 6. What is the sum of \(p\) and \(q\)?
- A 12
- B 14
- C 16
- D 20
- E 28
Intermediate Mathematical Challenge 2012, Question 7. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 16
The primes in question are 5 and 11. The only primes smaller than 5 are 2 and 3. However \(p\) and \(q\) cannot be 2 and 8 nor 3 and 9 since neither 8 nor 9 is prime.
Solution © UK Mathematics Trust, from the IMC 2012 solutions. Longer versions with investigations: Solutions and investigations (PDF).