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’, how many enemies will each member of S have?


  1. \(n - 3\)
  2. \(\frac{1}{2}\left( {{n^2} - 3n - 2} \right)\)
  3. \(2n - 7\)
  4. \(\frac{1}{2}\left( {{n^2} - 5n + 6} \right)\)
  5. \(\frac{1}{2}\left( {{n^2} - 7n + 14} \right)\)

Correct Option:4

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