Quantitative Ability (Part 3 of 9)

Directions: Answer these questions on the basis of the information given below:

Let S be the set of all pairs (i, j) where 1 < i < j < n and n > 4. 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.

  1. For general n, how many enemies will each member of Shave?

    1. ½ (n2 − 7n + 14)

    2. n − 3

    3. ½ (n2 − 3n − 2)

    4. 2n − 7

    5. ½ (n2 − 5n + 6)

    Answer: e

  2. 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. ½ (n2 − 7n + 16)

    2. ½ (n2 − 5n + 8)

    3. 2n − 6

    4. 1/2n (n − 3)

    5. n − 2

    Answer: e