Direction Test
NMMS – Mental Ability Test (MAT)
1. Simple Explanation
The Direction Test checks your ability to visualize and follow a sequence of movements on a coordinate or grid system.
- You are given a starting point.
- A series of directions (N, S, E, W, NE, SW, …) and distances (steps, units, or time) are described.
- Your task is to determine the final position relative to the start or to another reference point.
It is essentially a 2‑D (sometimes 3‑D) mental‑geometry problem.
2. Key Points
| # | Concept | What to remember |
|---|---|---|
| 1 | Cardinal directions | N, S, E, W – 90° apart. |
| 2 | Intercardinal directions | NE, SE, SW, NW – 45° between the adjacent cardinals. |
| 3 | Relative movement | “Move 3 steps north” = +3 in y direction. |
| 4 | Coordinate system | Use a Cartesian plane: x axis (E–W), y axis (N–S). |
| 5 | Vector addition | Each move is a vector; add them to get net displacement. |
| 6 | Symmetry | Moving k steps north and then k steps south returns you to the start. |
| 7 | Shortcut tricks | – Opposite directions cancel. – Diagonal moves combine x and y: 1 step NE = ( +1 , +1 ). |
| 8 | Distance/angle | If only final direction is needed, compare sums of x and y. |
| 9 | Special cases | “Same direction” → same sign; “opposite” → opposite sign. |
| 10 | Mental rotation | For problems with “turn left/right” you need 90° rotations. |
3. Worked Example
Problem
A person starts at point O (0, 0).
They follow this sequence:
- Move 4 steps north.
- Move 3 steps east.
- Move 2 steps south‑east.
- Move 1 step west.
- Move 1 step north‑west.
Question: Where is the person relative to the starting point O?
Solution
| Step | Direction | Vector (Δx, Δy) | Accumulated (x, y) |
|---|---|---|---|
| 1 | North | (0, +4) | (0, +4) |
| 2 | East | (+3, 0) | (+3, +4) |
| 3 | South‑East | (+1, –1) | (+4, +3) |
| 4 | West | (–1, 0) | (+3, +3) |
| 5 | North‑West | (–1, +1) | (2, +4) |
Answer: Final position is 2 steps east and 4 steps north of the start – i.e., direction N E (north‑east).
Quick check:
*x‑sum = +2 (east), y‑sum = +4 (north).
Both positive → final direction is NE.
4. Quick Revision Summary
- Start with a coordinate frame.
- Translate each direction into a vector.
- N = (0, +1)
- S = (0, –1)
- E = (+1, 0)
- W = (–1, 0)
- NE = (+1, +1) … etc.
- Add all vectors.
- Interpret the result:
- If x > 0 → east; x < 0 → west.
- If y > 0 → north; y < 0 → south.
- Both non‑zero → intercardinal direction.
- Zero vector → back at start.
- Use cancellation: Opposite moves cancel out.
- Remember 90° turns when “turn left/right” appears.
5. Practice Problems (Try before checking the solutions)
-
Start at (0,0).
- 2 steps east.
- 3 steps north.
- 1 step south‑west.
- 4 steps north‑west.
Where are you?
-
A car moves 5 km north, turns right, moves 3 km, turns left, moves 2 km north.
What is the final displacement from the start? -
In a 5×5 grid, a person starts at the center.
They move 2 steps north, then 1 step east, then 3