Direction sense: Reasoning Ability Notes for SBI PO

Direction Sense – Reasoning Ability (SBI PO)

Why it matters
Direction sense questions test your spatial awareness, ability to follow sequences of turns, and to translate verbal or pictorial information into a final bearing. In competitive exams such as JEE‑Mains, JEE‑Advanced, and SBI PO, they appear in Logic & Analytical Reasoning and Quantitative Aptitude sections. Mastery of this topic reduces time and eliminates guesswork.

1. Core Concepts

Term	Meaning	Example
Cardinal Directions	N, S, E, W	“North” → 0°
Intermediate Directions	NE, SE, SW, NW	“North‑East” → 45°
Bearing	Exact angle measured clockwise from North	“Bearing 125°” = 125° east of north
Direction Sense	Relative sense of movement (e.g., “left”, “right”, “forward”, “backward”)	“He turned left” → 90° counter‑clockwise from previous heading
Absolute Direction	Fixed orientation in the world (e.g., “to the south”)	“Move to the south” = 180° from north
Relative Direction	Orientation with respect to another object or person	“Walk parallel to the bus”

2. Notation & Angles

Symbol	Value (degrees from North)	Equivalent in compass form
N	0°	360°
NE	45°	45°
E	90°	90°
SE	135°	135°
S	180°	180°
SW	225°	225°
W	270°	270°
NW	315°	315°

Rule of Thumb

Clockwise = increasing angle.
Counter‑clockwise = decreasing angle (or add 360° and then reduce to 0‑359°).

Turning Left / Right

Left = +90° (counter‑clockwise).
Right = –90° (clockwise).

Important: Many exam questions use “turns” that are multiples of 90°. For example, “turn left 3 times” = 3 × 90° = 270° counter‑clockwise.

3. Step‑by‑Step Strategy

Identify the Starting Point & Facing Direction
- Usually given as “John starts at point A facing North.”
- Assign angle θ₀ = 0° for North.
Read Each Instruction Carefully
- Convert “turn right” → subtract 90°.
- Convert “turn left” → add 90°.
- Convert “turn back” or “reverse” → add 180°.
- Convert “move forward 10 m” → keep direction unchanged.
Keep a Running Total of the Heading
- After every instruction, compute
  θ_next = (θ_current ± Δθ) mod 360°.
- The modulo operation ensures the heading stays within 0–359°.
Determine Final Direction
- Convert the final angle to a cardinal or intermediate direction.
- If the question asks for a bearing, give the exact degree.
Check for Tricky Situations
- Multiple Turns in One Sentence: e.g., “turn left, then right, then left.”
- Relative to Another Person/Vehicle: use the other’s heading as reference.
- Opposite Directions: “backward” means heading +180°.

4. Common Problem Types & Tricky Points

Problem Type	Key Insight	Common Pitfall
Fixed Sequence of Turns	Use a simple cumulative sum of angles.	Forget to take modulo 360°; sign errors.
Turns with Distance	Distance does not affect direction; only turns do.	Assuming distance changes bearing.
Relative Turns	Convert relative instruction to absolute by adding/subtracting the other’s heading.	Mixing up “left of” vs “right of.”
Multiple Persons/Objects	Track each person’s heading separately.	Mistaking the reference frame (e.g., “to his right” vs “to my right”).
Direction between Two Points	Sometimes the question asks for the direction from point A to B, not the final heading of the mover.	Confusing the mover’s final heading with the direction from A to B.
Intermediate Directions	45°, 135°, 225°, 315° correspond to NE, SE, SW, NW respectively.	Misidentifying NE as “north‑east” but giving 225° (that’s SW).

5. Example Derivation

Problem:

A cyclist starts at point P facing East. He rides 5 km, turns left, rides 3 km, turns right, rides 4 km, turns left, and rides 2 km. What is his final heading?

Solution

Start: Facing East → θ₀ = 90°.
Turn left: θ₁ = 90° + 90° = 180° (South).
Turn right: θ₂ = 180° – 90° = 90° (East).
Turn left: θ₃ = 90° + 90° = 180° (South).

Final heading: South (180°).

Note: Distances (5 km, 3 km, …) don’t influence the heading.

6. Hard Practice Question (Competitive Level)

Question

Ravi starts at