GK 2017 Q13
13. Rohan wants to cut a piece of string into nine pieces of equal length. He marks his cutting points on the string. Jai wants to cut the same piece of string into only eight pieces of equal length. He marks his cutting points on the string. Yuvraj then cuts the string at all the cutting points that are marked. How many pieces of string does Yuvraj obtain?
- A 15
- B 16
- C 17
- D 18
- E 19
Grey Kangaroo 2017, Question 13. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 16
Rohan wants to obtain 9 equal pieces and so makes eight marks. Jai wants to obtain 8 equal pieces and so makes seven marks. Since 9 and 8 have no common factors (9 and 8 are co-prime), none of the marks made by either boy coincide. Therefore Yuvraj will cut at 15 marked points and hence will obtain 16 pieces of string.
Solution © UK Mathematics Trust, from the GK 2017 solutions.