IMC 2013 Q12
12. The sum
one + four = seventy
becomes correct if we replace each word by the number of letters in it to give 3 + 4 = 7.
Using the same convention, which of these words could be substituted for \(x\) to make the sum
three + five = \(x\) true?
- A eight
- B nine
- C twelve
- D seventeen
- E eighteen
Intermediate Mathematical Challenge 2013, Question 12. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D seventeen
As the words ‘three’ and ‘five’ contain 5 and 4 letters respectively, their ‘sum’ will be a 9-letter word. Of the alternatives given, only ‘seventeen’ contains 9 letters.
Solution © UK Mathematics Trust, from the IMC 2013 solutions. Longer versions with investigations: Solutions and investigations (PDF).