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1970 AMC 12 Question 9

AMC12 · 1970 AMC 12

Question 9

Points $P$ and $Q$ are on line segment $AB,$ and both points are on the same side of the midpoint of $AB.$ Point $P$ divides $AB$ in the ratio $2:3,$ and $Q$ divides $AB$ in the ratio $3:4.$ If $PQ=2,$ then the length of segment $AB$ is:
  1. $12$
  2. $28$
  3. $70$
  4. $75$
  5. $105$