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SMO 2025 Junior Round 1 Question 3

SMO · SMO 2025 Junior Round 1

Question 3

It is given that the equation
$$\left[\frac{5x-2}{3}\right]=\frac{7x-31}{2}$$
has two distinct solutions $\alpha$ and $\beta$. Find $[\alpha+\beta]$.
  1. 9
  2. 12
  3. 15
  4. 18
  5. 21