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IMAS 2018 Junior Round 1 Question 15

IMAS · IMAS 2018 Junior Round 1

Question 15

Starting from $\frac34$, add 2 to the numerator or add 3 to the denominator for each operation, but not both, and no reduction is performed. At least how many operations one needs to get a fraction again that is of the same value as $\frac34$?
  1. 13
  2. 17
  3. 20
  4. 26
  5. 34