Direction sense: Reasoning Ability Notes for Chandigarh Patwari / Lekhpal

Direction Sense – Reasoning Ability

Target Exam – Chandigarh Patwari / Lekhpal
Topic – Direction Sense (also called Relative Positioning or Positioning)

1. Simple Explanation

Direction sense tests your ability to interpret statements about the relative positions of objects or persons.
You often get a set of clues such as “A is to the left of B” or “C is north‑east of D” and have to deduce the final arrangement.

Key Idea
Treat each statement as a constraint on a 2‑D grid (or a mental map). Place the first item, then use the clues to place the others while maintaining all constraints.

2. Key Points

#	Concept	Why it matters
1	Cardinal & Intercardinal directions	4 basics (N, S, E, W) + 4 diagonals (NE, SE, SW, NW)
2	Relative terms	Left of / Right of (same row), Above / Below (same column), North‑East of etc.
3	Same line vs. same column	“to the left of” → same row, “to the north of” → same column
4	Opposite direction	If A is left of B, then B is right of A.
5	Transitivity	If A is left of B and B is left of C, then A is left of C.
6	Multiple constraints	If two statements contradict, discard the impossible arrangement.
7	Grid size	Usually 3×3 or 3×4; if not specified, assume the smallest grid that satisfies all clues.
8	Use of “between”	“A is between B and C” → B – A – C in a straight line (row or column).
9	Clues may be indirect	“D is north of E, and F is south of E” → D and F are on opposite sides of E.
10	Checking consistency	After placing all, re‑read clues to confirm no violation.

3. Worked Example

Problem

Five people – A, B, C, D, E – are standing in a 3×3 grid (rows 1–3 from top to bottom, columns 1–3 from left to right).
You are given the following clues:

A is to the left of B.

C is directly above B.

D is to the right of E.

E is at the bottom row.

C is in the middle column.

A is on the same row as D.

Question: Determine the exact positions of A–E.

Step‑by‑Step Solution

Step	Action	Reasoning
1	Place E on the bottom row.	Clue 4 says E is on the bottom.
2	Place D to the right of E.	Clue 3: D right of E.
3	Since E is on bottom row, D must also be on bottom row.	Same row implied by “to the right of”.
4	Place C in the middle column.	Clue 5.
5	C is directly above B → B is below C in same column.	Clue 2.
6	A is to the left of B → A left of B in same row.	Clue 1.
7	A is on same row as D.	Clue 6.
8	Since D is on bottom row, A must also be on bottom row.	Row restriction.
9	Bottom row already has D and E. The only remaining cell is column 2 (middle column). Place A there.	Filling empty spot.
10	A left of B ⇒ B must be in column 3 (right of A).	Column 3 now for B.
11	C is in middle column (column 2). B is below C (same column). So C must be in row 1, column 2.	Placement of C.
12	B below C → B occupies row 2, column 2.	But row 2 column 2 is already taken by A. Conflict!
13	Re‑check: We mis‑placed A. A must be on bottom row, but column 2 is already used by A. Therefore B cannot be below C in column 2.	We need to revisit assumption.
14	Alternative: C could be in column 2 but in row 3? No, bottom row is occupied by D and E.
15	Therefore our assumption that A is on bottom row is wrong? But clue 6 says A same row as D; D is bottom row. So A must be bottom row.
16	The only way is to adjust earlier assumption: C cannot be in column 2 if B must be below C. Wait: B below C → B is below C, not necessarily same column? Actually “directly above” means same column. So B must be below C in same column.
17	We realize the grid must be 3×3; bottom row cells are (3,1), (3,2), (3,3). We placed D (3,