GK 2017 Q12
12. Ellie wants to write a number in each box of the diagram shown. She has already written in two of the numbers. She wants the sum of all the numbers to be 35, the sum of the numbers in the first three boxes to be 22, and the sum of the numbers in the last three boxes to be 25.
| 3 | 4 |
What is the product of the numbers she writes in the shaded boxes?
- A 0
- B 39
- C 48
- D 63
- E 108
Grey Kangaroo 2017, Question 12. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 63
Since the sum of the numbers in the first three boxes is to be 22, the sum of the numbers in the last three boxes is to be 25 and the sum of the numbers in all five boxes is to be 35, Ellie will write (22 + 25 − 35) = 12 in the middle box. Therefore she will write (22 − 3 − 12) = 7 in the second box and (25 − 12 − 4) = 9 in the fourth box. Hence the product of the numbers in the shaded boxes is 7 × 9 = 63.
Solution © UK Mathematics Trust, from the GK 2017 solutions.