IMC 2005 Q5
5. How many of the statements in the box are true?
| Any number which is divisible by 6 is even. | Any number which is divisible by 9 is odd. |
| The sum of any two odd numbers is even. | The sum of any two even numbers is odd. |
- A 0
- B 1
- C 2
- D 3
- E 4
Intermediate Mathematical Challenge 2005, Question 5. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 2
If a number is divisible by 6 then it must also be divisible by 2, so is even. ‘The sum of any two odd numbers is even’ is also true. However, not all multiples of 9 are odd (e.g. 18) and the sum of any two even numbers is even rather than odd, so two of the four statements are true.
Solution © UK Mathematics Trust, from the IMC 2005 solutions.