Direction sense — Point X is in which direction with respect to Y? Statements: I. Point Z is at equal distance from both X and Y. II. From X, walk 5 km east; turn right and walk 5 km; turn right again and walk 5 km to reach Y.
Verbal Reasoning
Data Sufficiency
Difficulty: Medium
Choose an option
Answer
Correct Answer: Statement II alone is sufficient; Statement I alone is not sufficient.
Explanation
Introduction / Context:Find the relative direction of X from Y using movement instructions.
Given Data / Assumptions:
- I: Z is equidistant from X and Y (a locus statement; says nothing about bearing).
- II: Path from X → (E 5) → right (S 5) → right (W 5) = Y.
Concept / Approach:Resolve net displacement from X to Y using vector addition.
Step-by-Step Solution:
From II: Starting at X=(0,0): go to (5,0); right → south to (5,-5); right → west to (0,-5). Thus Y=(0,-5).Therefore, from Y to X is north by 5 km; equivalently, X is north of Y.Statement I alone defines a perpendicular bisector set; direction cannot be inferred.Verification / Alternative check:Sketching confirms a down-and-back Γ path ending directly south of start.
Why Other Options Are Wrong:
- I alone: infinite possibilities; no direction.
- Either alone / Both together not sufficient / Both together sufficient: incorrect because II alone already yields a unique direction.
Common Pitfalls:Mistaking 'right' turn orientation; forgetting that right after heading east points south.
Final Answer:Statement II alone is sufficient; Statement I alone is not sufficient. (X is north of Y.)