IMC 2014 Q2
2. Which is the smallest positive integer for which all these are true?
(i) It is odd.
(ii) It is not prime.
(iii) The next largest odd integer is not prime.
- A 9
- B 15
- C 21
- D 25
- E 33
Intermediate Mathematical Challenge 2014, Question 2. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 25
The first four options are the smallest positive integers which are both odd and not prime. However, the next largest odd numbers after 9, 15, 21 are 11, 17, 23 respectively and these are all prime. The next largest odd number after 25 is 27, which is not prime. So 25 is the smallest positive integer which satisfies all three conditions.
Solution © UK Mathematics Trust, from the IMC 2014 solutions. Longer versions with investigations: Solutions and investigations (PDF).