Consider the questions and two statements given below in respect of three cities P, Q and R is 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 statements?

EXPLANATION

Correct Option

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

Statement 1 provides the distance between city Q and city R: Q is 18 km from R.

Statement 2 provides the distance between city P and city R: P is 43 km from R.

Even when both statements are considered together, the relative positions of cities P and Q with respect to city R are not specified. The cities could be arranged linearly in different configurations:

If city R is between city P and city Q (e.g., P-R-Q or Q-R-P), the distance between P and Q would be the sum of their distances from R: 43 km + 18 km = 61 km.
If city R is not between city P and city Q (e.g., P-Q-R or Q-P-R, or R-P-Q or R-Q-P), and they are collinear, the distance between P and Q would be the absolute difference of their distances from R: |43 km - 18 km| = 25 km.

Since two distinct distances (61 km and 25 km) are possible based on the given information, both Statement 1 and Statement 2 together are not sufficient to uniquely determine the distance between city P and city Q.

Incorrect Options

Statement 1 alone is insufficient because it only provides the distance between Q and R (18 km). No information about city P is given, making it impossible to determine the distance between P and Q.

Statement 2 alone is insufficient because it only provides the distance between P and R (43 km). No information about city Q is given, making it impossible to determine the distance between P and Q.

Both Statement 1 and Statement 2 are not sufficient to answer the question, as explained above. The lack of information regarding the relative collinear arrangement of the three cities leads to multiple possible distances between P and Q.