Logical Analysis

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.

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  Statement I alone ("T and U are at the ends"): This gives two possibilities (T...U or U...T) but doesn't identify the person in the 4th spot. This statement is not sufficient.
  


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  Statement II alone ("S is third to the right of T"): This gives a relative block of four people (T _ _ S) but not their absolute positions in the main row. This statement is not sufficient.
  


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  Combining Statements I and II:
  
  
  
  • If the row starts with U and ends with T (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.
  
  
  • If the row starts with T and ends with U (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.