Quantitative Ability (Part 3 of 9)

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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. (n2 − 7n + 14)
    2. n − 3
    3. (n2 − 3n − 2)
    4. 2n − 7
    5. (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. (n2 − 7n + 16)
    2. (n2 − 5n + 8)
    3. 2n − 6
    4. n (n − 3)
    5. n − 2

    Answer: e

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