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Australian AMC 2023 - Upper Primary Question 21

AMC AUSTRALIA · Australian AMC 2023 - Upper Primary

Question 21

Mrs Graaf invents a game for her students to practise arithmetic. They roll two 10-sided dice to pick two random numbers. Starting at one of the numbers, they keep adding the other number until they reach a 3-digit number.
Ian rolls a 5 and an 8. Starting with 5 and repeatedly adding 8 gives 5,13,21,…,93,101. Starting with 8 and adding 5 gives 8,13,18,…,98,103.
On Nara’s turn, she makes a list that ends with 107. What pair of numbers could she have rolled?

Question illustration
  1. 4 and 8
  2. 5 and 7
  3. 3 and 4
  4. 6 and 9
  5. 3 and 8