Direction sense — What is the direction of tower P with respect to tower Q? Statements: I. P is to the west of H, and H is to the south of Q. II. F is to the west of Q and to the north of P.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:We must determine the direction of P with respect to Q using two spatial statements. Direction-sense DS questions test whether a unique conclusion is implied without assuming distances or collinearity. Given Data / Assumptions: I: P is west of H; H is south of Q. II: F is west of Q and north of P. Standard compass directions; distances are unspecified. Concept / Approach:Translate each statement to relative quadrants. With no distances, multiple placements can satisfy the constraints. We need uniqueness for a sufficient conclusion. Step-by-Step Solution: From I: Place Q at origin. H must be somewhere directly south of Q. P lies somewhere west of H. Hence, P is south-west of Q or at least west and south relative to Q, but the exact bearing (W, SW, SSW, etc.) depends on distances. Direction from P to Q is therefore ambiguous using I alone.From II: F is west of Q and north of P. This places P south of F, but P's position relative to Q can vary widely; P could be anywhere south of F while F remains west of Q.Combining I and II still allows multiple valid layouts. Example A: Let Q=(0,0), H=(0,-1), P=(-1,-1). Choose F=(-1,0). Example B: Q=(0,0), H=(0,-3), P=(-4,-3), F=(-4,-2). In A, Q is NE of P; in B, Q is ENE of P—different specific directions. Verification / Alternative check:Try to force a single compass word (e.g., 'north-east'). Distances remain free variables, so uniqueness fails. Why Other Options Are Wrong: I alone: does not fix distances; multiple directions possible. II alone: gives only relative info via F; P vs Q undetermined. Either alone sufficient: false for the reasons above. Both together sufficient: still multiple arrangements exist. Common Pitfalls:Assuming equal distances or grid alignment that is not stated; reading 'west of' as a fixed offset; forcing diagonals without necessity. Final Answer:Both Statements I and II together are not sufficient.

Direction sense — What is the direction of tower P with respect to tower Q? Statements: I. P is to the west of H, and H is to the south of Q. II. F is to the west of Q and to the north of P.

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