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IMAS 2023–2024 — Upper Primary — Round 2 Question 2

IMAS · IMAS 2023–2024 — Upper Primary — Round 2

Question 2

John takes a number and intends to multiply it with the two-digit number $\overline{ab}$, but he mistakenly multiplies it with $\overline{ba}$. If $b>a$ and the difference between the correct result and the mistaken result is 819, what is the sum of all possible values of John’s number?
  1. 103
  2. 104
  3. 105
  4. 106
  5. 107