GK 2020 Q7
7. Each cell of a 3 × 3 square has a number written in it. Unfortunately the numbers are not visible because they are covered in ink. However, the sum of the numbers in each row and the sum of the numbers in two of the columns are all known, as shown by the arrows on the diagram. What is the sum of the numbers in the third column?
- A 41
- B 43
- C 44
- D 45
- E 47
Grey Kangaroo 2020, Question 7. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 43
The sum of the row totals is the sum of all the nine numbers in the 3 × 3 square. Likewise, the sum of the column totals is the sum of these nine numbers. Therefore \(24 + 26 + 40 = 27 + 20 + x\), where \(x\) is the sum of the numbers in the third column. Therefore \(90 = 47 + x\) and hence \(x = 43\). Therefore the sum of the numbers in the third column is 43.
Solution © UK Mathematics Trust, from the GK 2020 solutions.