PK 2016 Q3
3. When the positive integer \(x\) is divided by 6, the remainder is 3. What is the remainder when \(3x\) is divided by 6?
- A 4
- B 3
- C 2
- D 1
- E 0
Pink Kangaroo 2016, Question 3. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 3
The number \(x\) is 3 more than a multiple of 6, so \(x = 6k + 3\) for some non-negative integer value of \(k\). And then
\(3x = 3(6k + 3) = 18k + 9 = 6(3k + 1) + 3\). Hence \(3x\) is 3 more than a multiple of 6, so leaves remainder 3 when divided by 6.
Solution © UK Mathematics Trust, from the PK 2016 solutions.