CAT Quant Practice Problems

Question: Let S be the set of all pairs (i, j) where, 1≤ i < j ≤ n and n≥ Any two distinct members of S are called “friends” if they have one constituent of the pairs in common and “enemies” otherwise. For example, if n = 4, then S = {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}. Here, (1, 2) and (1, 3) are friends, (1, 2) and (2, 3) are also friends, but (1, 4) and (2, 3) are enemies.

For general ‘n’, consider any two members of S that are friends. How many other members of S will be common friends of both these members?


  1. \(\frac{1}{2}\left( {{n^2} - 5n + 8} \right)\)
  2. \(2n - 6\)
  3. \(\frac{1}{2}n\left( {n - 3} \right)\)
  4. \(n - 2\)
  5. \(\frac{1}{2}\left( {{n^2} - 7n + 16} \right)\)

Correct Option:4

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