GK 2016 Q6
6. Two pieces of rope have lengths 1 m and 2 m. Alex cuts the pieces into several parts. All the parts have the same length. Which of the following could not be the total number of parts he obtains?
- A 6
- B 8
- C 9
- D 12
- E 15
Grey Kangaroo 2016, Question 6. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 8
Since all the parts cut are of the same length, Alex will obtain twice as many parts from his 2 metre piece of rope as he does from his 1 metre piece of rope. Hence, the total number of parts he obtains will always be a multiple of 3, and he can make it any multiple of 3. Of the options given, only 8 is not a multiple of 3 and so could not be obtained.
Solution © UK Mathematics Trust, from the GK 2016 solutions.