GK 2018 Q9
9. Martha multiplied two 2-digit numbers correctly on a piece of paper. Then she scribbled out three digits as shown.
What is the sum of the three digits she scribbled out?
- A 5
- B 6
- C 9
- D 12
- E 14
Grey Kangaroo 2018, Question 9. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 6
Let the three missing digits from left to right be \(a\), \(b\) and \(c\). Consider the final digit ‘2’ of the answer. This is the last digit of \(3 \times b\) and hence \(b = 4\). Also, note that if \(a\) were 2 or more, then the answer would be more than 400. Therefore \(a = 1\). Hence the multiplication is 13 × 24 = 312, giving \(c = 1\). Therefore the sum of the digits scribbled out is \(a + b + c = 1 + 4 + 1 = 6\).
Solution © UK Mathematics Trust, from the GK 2018 solutions.