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?

The question asks for the distance between city P and city Q (PQ).

Statement 1: "City Q is 18 km from city R." This tells us the distance QR = 18 km. This statement alone does not provide any information about city P, so it is not sufficient to find the distance PQ.

Statement 2: "City P is 43 km from city R." This tells us the distance PR = 43 km. This statement alone does not provide any information about city Q, so it is not sufficient to find the distance PQ.

Combining both Statement 1 and Statement 2: We know QR = 18 km and PR = 43 km. The relative positions of P, Q, and R are not specified (e.g., whether they are collinear or form a triangle).

Case 1: The cities are collinear (lie on a straight line). a) If Q is between P and R (P - Q - R): Then PR = PQ + QR 43 = PQ + 18 PQ = 43 - 18 = 25 km.

b) If R is between P and Q (P - R - Q): Then PQ = PR + RQ PQ = 43 + 18 = 61 km.

c) If P is between Q and R (Q - P - R): Then QR = QP + PR 18 = QP + 43 QP = 18 - 43 = -25 km, which is impossible as distance cannot be negative. This arrangement is not valid.

Since there are two distinct possible distances (25 km or 61 km) even if the cities are collinear, the information is not sufficient to give a unique answer.

Case 2: The cities are not collinear (they form a triangle PQR). In a triangle, the length of one side must be greater than the absolute difference of the other two sides and less than their sum. So, |PR - QR| < PQ < (PR + QR) |43 - 18| < PQ < (43 + 18) 25 km < PQ < 61 km. In this case, PQ could be any distance between 25 km and 61 km (e.g., 30 km, 45 km, 50 km, etc.), which means there are infinite possibilities.

Since neither statement alone nor both statements together provide a unique distance for PQ, both statements are not sufficient to answer the question.

The final answer is D