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SMO 2025 Junior Round 1 Question 4

SMO · SMO 2025 Junior Round 1

Question 4

Let $p=\frac{7a}{15}-1$ and $q=a^2-\frac{8a}{15}$, where $a$ is a real number. Which is the following statements is correct for any given value of $a$?
  1. $p>q$
  2. $p<q$
  3. $p=q$
  4. $20p>q$
  5. None of the above