IMC 2010 Q3
3. Exactly one of the following is a prime number. Which is it?
- A 2345
- B 23 456
- C 234 567
- D 2 345 678
- E 23 456 789
Intermediate Mathematical Challenge 2010, Question 3. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 23 456 789
2345 has units digit 5 and so is a multiple of 5; 23 456 is even; the digit sum of 234 567 is 27 so it is a multiple of 9; 2 345 678 is even. So if exactly one of the numbers is prime then it must be 23 456 789.
Solution © UK Mathematics Trust, from the IMC 2010 solutions.