Consider the Question and two Statements given below in respect of three cities P, Q and R in a State : Question : How far is city P from city Q? Statement-1 : City Q is 18 km from city R. Statement-2 : City P is 43 km from city R. Which one of the following is correct in respect of the Question and the Statements?

(a) Statement-1 alone is sufficient to answer the Question
(b) Statement-2 alone is sufficient to answer the Question
(c) Both Statement-1 and Statement-2 are sufficient to answer the Question
(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question ✓ UPSC's answer

Why the answer is (d)

• The Question asks for the distance between cities P and Q.

• Statement-1 gives only the Q–R distance (18 km), and Statement-2 gives only the P–R distance (43 km); neither alone mentions both P and Q.

• Together they fix how far P and Q each are from R, but not their directions. If P and Q lie on the same side of R in a straight line, PQ = 43 − 18 = 25 km; on opposite sides, PQ = 43 + 18 = 61 km; otherwise PQ can be anything in between.

• So even both statements together cannot answer the Question, option (d).

Why the other options are wrong

(a) Statement-1 alone is sufficient to answer the Question: Statement-1 only gives the distance between Q and R, providing no information about the location of P.
(b) Statement-2 alone is sufficient to answer the Question: Statement-2 only gives the distance between P and R, providing no information about the location of Q.
(c) Both Statement-1 and Statement-2 are sufficient to answer the Question: Combining both statements still leaves the relative positions of P and Q with respect to R unknown, making the distance between P and Q indeterminate.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2022, held on 5 June 2022. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.