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Australian AMC 2024 - Intermediate Question 17

AMC AUSTRALIA · Australian AMC 2024 - Intermediate

Question 17

When the number 9045 is split into two 2-digit numbers, the first number is twice the second number:90=2 × 45. Many other 4-digit numbers can be split into two 2-digit numbers where the first number is twice the second. There is a unique 2-digit number that divides into all such 4-digit numbers. What is this number?
  1. 18
  2. 35
  3. 45
  4. 52
  5. 67