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Quantitative Aptitude

Solving Inequalities

Let S be the ...

Question

Let S be the set of all pairs (i,j) where 1 $\leq$ i < j $\leq$ n and n $\geq$ 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), (1,3) are friends but (1,4), (2,3) are enemies.
For a general 'n', how many enemies will each member of S have?

\frac{n^{2} - 3 n - 2}{2}

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2 n - 7

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\frac{n^{2} - 5 n + 6}{2}

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\frac{n^{2} - 7 n + 14}{2}

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Solution

The correct option is C $\frac{n^{2} - 5 n + 6}{2}$
Option (C) is the correct answer. Check the video for the approach.

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Similar questions

A_{1}, A_{2}, . . . . . A_{n}

are thirty sets, each with five elements and

B_{1}, B_{2}, . . . . B_{n}

are

n

sets, each with three elements.
Let

⋃_{i = 1}^{30} A_{i} = ⋃_{j = 1}^{n} B_{j} = S

. If each element of

S

belongs to exactly ten of

A_{i}

's and exactly nine of the

B_{j}

's, then

n

Q. Suppose

A_{1}, A_{2},, A_{30}

are thirty sets each having

5

elements and

B_{1}, B_{2}, . ., B_{n}

are

n

sets each with

3

elements, let

30 ⋃ i = 1 A_{i} = n ⋃ j = 1 B_{j} = S

and each element of

S

belongs to exactly

10

of the

A_{i} s

and exactly

9

of the

B_{j} s .

Then

n

is equal to

Suppose $A_{1}, A_{2}, . . ., A_{30}$ are thirty sets, each with five elements and $B_{1}, B_{2}, . . ., B_{30}$ are $n$ sets ecah with three elements. Let $30 ⋃ i = 1 A_{i} = n ⋃ j = 1 B_{j} = S$

If each element of $S$ belongs to exactly ten of the $A_{i}^{'} s$ and exactly none of the $B_{j}^{'} s$ then $n =$

Q. Let A [1...n] be any array of n distinct numbers, If i < j and A [i] > A[j], then the pair (i,j) is called an inversion of A. What is the expected number of inversion in any permutation on n elements?

A_{1}, A_{2}, \dots, A_{30}

are

30

sets, each having

5

elements and

B_{1}, B_{2}, \dots, B_{n}

are

n

sets each with

3

elements. If

30 ⋃ i = 1 A_{i} = n ⋃ j = 1 B_{j} = S

and each element of

S

belongs to exactly

10

of the

A_{i}

's and exactly

9

of the

B_{j}

's, then the value of

n

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The correct option is C n2−5n+62Option (C) is the correct answer. Check the video for the approach.

The correct option is C $\frac{n^{2} - 5 n + 6}{2}$
Option (C) is the correct answer. Check the video for the approach.