P, Q, R, S, T, U and V are sitting in a row facing North. In order to determine, who is sitting exactly in the middle of the row, which of the following information is needed?
(I) T and U are sitting at extreme ends of the row
(II) S is third to the right of T
(III) Q is four places to the left of R and P is two places to the left of V
Step-by-step Solution:
The goal is to find the person in the middle of a 7-person row, which is the 4th position. We need to find the minimum information required to identify this person.
T...U or U...T) but doesn't identify the person in the 4th spot. This statement is not sufficient.T _ _ S) but not their absolute positions in the main row. This statement is not sufficient.U _ _ _ _ _ T), it's impossible to place S "third to the right of T" as it would be outside the row. This arrangement is invalid.T _ _ _ _ _ U), we can place the T _ _ S block. This forces T into position 1 and S into position 4.This combination leads to the definite conclusion that S is in the middle. Therefore, statements I and II together are sufficient.
Since statements I and II together are sufficient to answer the question, we have found the minimum required information.
Final Answer: The correct option is A. I and II only are sufficient.