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CAT 2016 | Question: 98

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There are $12$ towns grouped into four zones with three towns per zone. It is intended to connect the towns with telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required?

  1. $72$
  2. $90$
  3. $96$
  4. $144$
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