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Australian AMC 2022 - Senior Question 11

AMC AUSTRALIA · Australian AMC 2022 - Senior

Question 11

The operation $\divideontimes$ is defined by $p\divideontimes q=2p-q$. Each of $p$ and $q$ is an integer from $-6$ to $+6$. How many pairs of values $(p,q)$ will have $p\divideontimes q=q\divideontimes p$?
  1. 6
  2. 13
  3. 36
  4. 49
  5. 169