Consider the Question Statements given below in respect of and two 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.

Statement 1: City Q is 18 km from city R. This statement gives us the distance QR = 18 km. It provides no information about city P. Therefore, Statement 1 alone is not sufficient to determine the distance PQ.

Statement 2: City P is 43 km from city R. This statement gives us the distance PR = 43 km. It provides no information about city Q's position relative to P or R's position relative to Q. Therefore, Statement 2 alone is not sufficient to determine the distance PQ.

Combining both Statement 1 and Statement 2: We know QR = 18 km and PR = 43 km. We need to find PQ. There are multiple possible arrangements for the three cities P, Q, and R:

1. If Q is located between P and R (P-Q-R): Then PQ + QR = PR. So, PQ + 18 = 43, which means PQ = 43 - 18 = 25 km.
2. If R is located between P and Q (P-R-Q): Then PR + RQ = PQ. So, 43 + 18 = PQ, which means PQ = 61 km.
3. If the three cities form a triangle (not collinear): In this case, the distance PQ would be a side of a triangle with other sides 18 km and 43 km. According to the triangle inequality theorem, the third side (PQ) must be greater than the absolute difference of the other two sides and less than their sum. So, |43 - 18| < PQ < (43 + 18), which means 25 km < PQ < 61 km.

Since we can get different possible distances for PQ (25 km, 61 km, or any value between 25 km and 61 km if they form a triangle), the information provided by both statements together is not sufficient to determine a unique distance between city P and city Q.

Therefore, both Statement-1 and Statement-2 are not sufficient to answer the Question.

The final answer is D