Question

Among four students - P, Q, R and S, no two students got the same marks and each of them is either a liar or a truth-teller. A liar is one who always lies and a truth teller is one who always tells the truth. Who got the highest mark?
I. Each one of them claims that he got the highest mark. Between R and S, there is exactly one person who always lies.
II. P says, "neither Q nor S got the highest mark."

• A. If the question can be answered by any one of the statements alone, but cannot be answered by using the other statement alone.
• B.

  If the question can be answered by using either statement alone.

• C. If the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
• D. If the question cannot be answered even by using both the statements together.

Answer 1

The correct option is C If the question can be answered by using both the statements together, but cannot be answered by using either statement alone.

From statement (I) alone, we know only one among P, Q, R and S is a truth teller. Between R and S there is exactly one person who always lies means the other person is a truth teller. The remaining two persons P and Q are liars. So, either R or S gets the highest mark.
From statement (II) alone, we do not know whether P is a liar or a truth-teller.
So, statement (II) alone is not sufficient.
Combining statement (I) and (Ii), we get P is a liar and he says neither Q nor S got the highest mark which implies that either Q or S gets the highest mark. But from statement (I), Q is a liar. Hence, S gets the highest mark.
Both statements are necessary to answer the question.