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Seven people P, Q, R, S, T, U and V are standing in a queue. The number of people standing in front of P and V is same as the number of people standing behind R and S respectively. Three people are standing between Q and U. Q is standing behind P, but ahead of T. Who is standing at the rear end of the queue?

Seven people P, Q, R, S, T, U and V are standing in a queue. The number of people standing in front of P and V is same as the number of people standing behind R and S respectively. Three people are standing between Q and U. Q is standing behind P, but ahead of T. Who is standing at the rear end of the queue? Correct Answer R

Let us indicate the positions in the queue from the front end to the rear end as follows:

1

2

3

4

5

6

7

1) The number of people standing in front of P is same as the number of people standing behind R respectively → The possible positions of P and R are (1 and 7) or (2 and 6) or (3 and 5).

2) The number of people standing in front of V is same as the number of people standing behind S respectively → The possible positions of V and S are (1 and 7) or (2 and 6) or (3 and 5).

3) Three people are standing between Q and U → The possible positions of Q and U are (1 and 5), (2 and 6) and (3 and 7).

4) From the above discussion it is clear that P, Q, R, S, U and V cannot occupy position 4. Hence, T occupies position 4.

 

1

2

3

4          T

5

6

7

 

5) If Q and U occupy position (1 and 5) then P and R must be in position (2 and 6). In such case we cannot find position for V and S.

6) Similarly, if Q and U occupy position (3 and 7) then P and R must be in position (2 and 6). In such case we cannot find position for V and S.

7) Hence, Q and U occupy position (2 and 6).

 

1         

2          Q/U

3

4          T

5

6          Q/U

7         

 

8) Q is standing behind P, but ahead of T → Q is at 2nd position from the front end. P and R will occupy position (1 and 7) respectively.

 

1          P

2          Q

3         

4          T

5

6          U

7          R

 

9) V and S would occupy position 2 and 5 respectively.

 

1          P

2          Q

3          V

4          T

5          S

6          U

7          R

Clearly, R is standing at the rear end of the queue.

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