Which village is to the North East of village M? I. Village S is to the South…

Concept: In a direction-sense data-sufficiency question, a plain cardinal relation ('north of', 'south of', 'east of', 'west of') fixes one shared coordinate between two points (same longitude for north–south, same latitude for east–west), while a compound relation ('north-east of', 'south-west of', etc.) only fixes both coordinates to be strictly greater or smaller in each direction, without pinning an exact distance. A statement pair is sufficient here only if, after plotting it on a shared grid using a common village as the link between the two statements, the target village's direction relative to the reference follows from these strict inequalities alone – even when the exact distances are never given.

1. Statement I places Z at the centre, S to its South-East, and B to its North-East; since B is also north of Q, Q sits directly below B on the same longitude.

   

2. Statement I never mentions village M, so on its own it cannot fix any direction from M.

3. Statement II places Q at the centre, B directly above it (north of Q), and T to Q's North-West.

   

4. Statement II also leaves village M completely unplaced, so it too is insufficient alone.

5. Statement III places M in the centre of the row Z–M–Q (Z to its west, Q to its east, all on one latitude), with S directly south of M.

   

6. Statement III places S, Z and Q relative to M (south, west, and east respectively), but none of these three is to M's North-East, and it never places B or T at all – so it cannot answer the question by itself either.

7. Combining I and III through the shared village S: aligning S's position from both statements shows Q sits east of M's row and B sits on Q's longitude but north of it – so B lies strictly east of M and strictly north of M, i.e., to its North-East.

   

8. Combining II and III through the shared village Q: aligning Q's position from both statements again places B on Q's longitude (east of M's row) and north of Q – so B is once again strictly east and north of M, i.e., to its North-East.

   

Cross-check: both independent combinations – (I & III) and (II & III) – land on the exact same relation (B is North-East of M), which is exactly why either pair alone is enough; you never need all three statements together. (Village T's own position is fixed only relative to Q, not directly to M; sketching each relation as a single step, exactly as in the figures, places T due north of M, so B remains the sole village to M's North-East.)

Hence the question is answered by using either Statement I with III, or Statement II with III – matching the option 'Only I and III or only II and III are required to answer the question.'