IMC 2013 Q1
1. Which of the following is divisible by 6?
- A one million minus one
- B one million minus two
- C one million minus three
- D one million minus four
- E one million minus five
Intermediate Mathematical Challenge 2013, Question 1. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D one million minus four
In order to be a multiple of 6, a number must be both even and a multiple of 3. Of the numbers given, only B 999 998 and D 999 996 are even. Using the rule for division by 3, we see that, of these two, only 999 996 is a multiple of 3.
Solution © UK Mathematics Trust, from the IMC 2013 solutions. Longer versions with investigations: Solutions and investigations (PDF).