PK 2020 Q4
4. The sum of four consecutive integers is 2. What is the least of these integers?
- A −3
- B −2
- C −1
- D 0
- E 1
Pink Kangaroo 2020, Question 4. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C −1
The four integers cannot all be non-positive since the total is positive. Also, they cannot all be non-negative since the smallest possible total would then be 0 + 1 + 2 + 3 = 6. So, they must have at least one negative integer, and at least one positive integer, and hence will include -1, 0 and 1. Since these have a total of 0, the fourth number must be 2. Thus the least integer is -1.
Solution © UK Mathematics Trust, from the PK 2020 solutions.