PK 2019 Q9
9. On each of three pieces of paper a five-digit number is written as shown.
Three of the digits are covered. The sum of the three numbers is 57263.
What are the covered digits?
- A 0, 2 and 2
- B 1, 2 and 9
- C 2, 4 and 9
- D 2, 7 and 8
- E 5, 7 and 8
Pink Kangaroo 2019, Question 9. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 1, 2 and 9
Let the missing digits be \(P\), \(Q\), \(R\). Placing the numbers in a column addition, we get:
| 1 | 5 | 7 | 2 | 8 | |
| 2 | 2 | P | 0 | 4 | |
| + | Q | R | 3 | 3 | 1 |
| 5 | 7 | 2 | 6 | 3 |
There is nothing to carry from the sum of the tens digits, so the sum of the middle digits is \(7 + P + 3\) and this must end in 2. Hence \(P = 2\). The sum of the digits in the next column is \(5 + 2 + R + 1\) (where the 1 is carried from the middle digits). This must end in a 7, giving \(R = 9\). The first digits have sum \(1 + 2 + Q + 1\) and must end in 5 so \(Q = 1\). Therefore the missing digits are 1, 2, 9.
Solution © UK Mathematics Trust, from the PK 2019 solutions.