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Q3637/80Q38
Q37·CSAT · Prelims 2022

Data sufficiency for determining distance using collinear vs non-collinear points

DI / DSDirection & DistanceFactual singleMedium

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

a

Statement-1 alone is sufficient to answer the Question

b

Statement-2 alone is sufficient to answer the Question

c

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

d

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

Answer

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.

If they are in a straight line: PQ could be 43 - 18 = 25 km, or 43 + 18 = 61 km.
If they form a right angle, PQ could be √(43² + 18²).

Since multiple distances are mathematically possible, the statements are insufficient even when combined.

In geometric distance puzzles, knowing the lengths of two sides of a triangle is never enough to find the third side unless the enclosed angle (or collinearity) is explicitly defined.

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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