**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?

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

## CAT Quant Questions with Video Solutions

- CAT Quant Questions Set 01
- CAT Quant Questions Set 02
- CAT Quant Questions Set 03
- CAT Quant Questions Set 04
- CAT Quant Questions Set 05
- CAT Quant Questions Set 06