Data sufficiency for determining distance using collinear vs non-collinear points
Question
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 Statement-1 and Statement-2 are not sufficient to answer the Question
Explanation
To determine the exact straight-line distance between P and Q, we need their relative vector coordinates. Statement 1 provides the radius distance QR = 18 km. Statement 2 provides the radius distance PR = 43 km.
These distances only establish that P and Q lie on circular perimeters around R. Because no directional angles or relative compass headings are provided, P, Q, and R could form an infinite number of triangles.
Since multiple distances are mathematically possible, the statements are insufficient even when combined.
Answer: (d).
Question details
Year
2022
Paper
CSAT
Question
Q37
Section
Data Interpretation & Sufficiency
Sub-topic
Direction & Distance
Type
Factual single
Difficulty
Medium
Source hint
How far is city P from city Q?
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