Question Details

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?

Options

Statement-1 alone is sufficient to answer the Question

Statement-2 alone is sufficient to answer the Question

Both Statement-1 and Statement-2 are sufficient to answer the Question

Both Statment-1 and Statement-2 are not sufficient to answer the Question

Show Answer

Correct Answer :

Option D

Both Statment-1 and Statement-2 are not sufficient to answer the Question

Solution :

The correct option is: Both Statment-1 and Statement-2 are not sufficient to answer the Question.

Let us analyze the information given in the statements to determine the distance between city P and city Q.
The question asks: How far is city P from city Q?

Analysis of Statement-1:
Statement-1 tells us that City Q is 18 km from city R. This gives us the distance between Q and R, but it provides no information about the location of city P. Therefore, Statement-1 alone is not sufficient to answer the question.

Analysis of Statement-2:
Statement-2 tells us that City P is 43 km from city R. This gives us the distance between P and R, but it provides no information about the location of city Q. Therefore, Statement-2 alone is not sufficient to answer the question.

Combining Statement-1 and Statement-2:
Even if we use both statements together, we only know the distances of cities P and Q from a common point, city R:
Distance(Q, R) = 18 km
Distance(P, R) = 43 km

However, we do not know the relative directions or positions of the three cities. They could be collinear (lying on the same straight line) or they could form a triangle. For instance:
1. If P, Q, and R lie on a straight line in the order P-R-Q, then the distance between P and Q would be:
$P Q = P R + R Q = 43 + 18 = 61 km$
2. If they lie on a straight line in the order P-Q-R, then the distance between P and Q would be:
$P Q = P R - R Q = 43 - 18 = 25 km$
3. If P, Q, and R form a triangle, the distance between P and Q could be any value strictly between:
$P R - R Q < P Q < P R + R Q$
which simplifies to:
$25 km < P Q < 61 km$

Since multiple distances are possible, we cannot determine a unique distance between city P and city Q. Thus, even together, the statements are not sufficient.