GK 2015 Q4
4. Which of the following numbers is not an integer?
- A \(\dfrac{2011}{1}\)
- B \(\dfrac{2012}{2}\)
- C \(\dfrac{2013}{3}\)
- D \(\dfrac{2014}{4}\)
- E \(\dfrac{2015}{5}\)
Grey Kangaroo 2015, Question 4. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D \(\dfrac{2014}{4}\)
The numbers in options A, B and E are clearly integers. In option C, 2 + 0 + 1 + 3 = 6 so, using the divisibility rule for divisibility by 3, \(\dfrac{2013}{3}\) is also an integer. However, while 2000 is divisible by 4, 14 is not so only \(\dfrac{2014}{4}\) is not an integer.
Solution © UK Mathematics Trust, from the GK 2015 solutions.