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Previous Year Questions

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Question :

Directions : Certain number of people were seated in a linear row facing north. Information about only some of them is known. Number of people seated between M and W is equal to the number of people seated between Q and N. S is fifth to the right of O. Four people were seated between W and R. T was seated second from the left end of the row and was not a neighbour of R. No three people whose information is known were seated together. O is seated eighth to the right of T. Not more than 25 people were seated in the row. Number of people seated to the right of N is one more than twice the number of people seated between R and W. Eight people were seated between W and Q where Q is seated to the right of W. As many people were seated to the left of M as were seated to the right of P. Only two people were seated between R and M. Five people are seated between N and P where P is to the right of N.

How many people were seated in the row?

1. 19

2. 24

3. 22

4. 23

5. None of these

Correct Answer : 3
Solution :

Eight people were seated between W and Q where Q is seated to the right of W.

Four people were seated between W and R. Only two people were seated between R and M who was not seated adjacent to Q.

Case 1:

Case 2:

Only two people were seated between R and M.

Case 1a:

Case 1b:

Case 2a:

Case 2b:

Number of people seated between M and W is equal to the number of people seated between Q and N.

Case 1a(i):

Case 1a(ii):

Case 1b (i):

Case 1b(ii):

Case 2a(i):

Case 2a(ii):

Case 2b:

Number of people seated to the right of N is one more than twice the number of people seated between R and W. Not more than 25 people were seated in the row.

So, case 1b(i), 2a(ii) are invalid.

Five people are seated between N and P where P is to the right of N.

Case 1a(i):

As many people were seated to the left of M as were seated to the right of P.

T was seated second from the left end of the row and was not a neighbour of R.

So, this case is invalid.

Case 1a(ii):

As many people were seated to the left of M as were seated to the right of P.

T was seated second from the left end of the row and was not a neighbour of R.

So, this case is invalid.

Case 1b(ii):

But no three people whose information is known were seated together. Hence this case is invalid.

Case 2a(i):

As many people were seated to the left of M as were seated to the right of P.

T was seated second from the left end of the row and was not a neighbour of R.

So, this case is invalid.

Case 2b:

O is seated eighth to the right of T. S is fifth to the right of O.

22 people were seated in the row.

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