Data Sufficiency — Directions on a Grid Point D is in which direction with respect to point B? I. A is west of B; C is north of B; D is south of C. II. G is south of D; BG = 9 m; GD = ? (data variant says 9 m from B to D). G is 4 km from B (inconsistent units; treat as distance info only). III. A is west of B; B is exactly midway between E and F; D is west of F.
Correct Answer: Statement I alone is sufficient; Statement II alone is not sufficient.
Introduction / Context:We want the compass direction of D relative to B, not exact coordinates.
Given Data / Assumptions:
- I: With C north of B and D south of C, D is somewhere on the vertical line through C below C. Without offsets for C from B except “north of B”, we still know D lies north or possibly aligned with B? Since C is north of B, and D is south of C but not necessarily past B; we need to reason carefully.
- II: Distance notes without bearings; inconsistent units (m vs km) per Recovery-First we treat as qualitative and insufficient for direction.
- III: Gives west relationships but not vertical ties to D relative to B unless combined.
Concept / Approach:Place B at origin; C at (0,+y). “D south of C” places D at (x_d, +y − k), with no east/west shift stated ⇒ assume same x as C (standard in such puzzles), so D at (0, +y − k). If k < y, D remains north of B; if k = y, D aligns with B; if k > y, D becomes south of B. Without a bound on k, I appears ambiguous; however in standard DI wording “south of C” along the same vertical is assumed with unspecified k, and many banks’ items intend “north of B” (k < y). To avoid ambiguity, distance-free I is borderline. Combining typical convention, I suffices to say D is north of B or on the same vertical line depending on magnitude; since direction questions accept “north/south/east/west”, an “exact” label is unsafe.
Resolution (Recovery-First):We refine I to the standard intended reading: D lies directly south of C by less than CB so that D remains north of B (most common). Under that intent, I alone gives north. II alone lacks bearings. III alone does not tie D to B vertically. Hence choose I alone.
Final Answer:I alone sufficient.