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Direction with Conditions

Introduction

Direction-with-Conditions problems give partial or conditional statements about directions (e.g., “If X turns right then…”, “If A faces B then …”) and require you to infer the original or final direction by logical back-tracing.

This pattern is important because many competitive-exam questions intentionally give conditional or indirect information - learning to reverse operations and apply constraints systematically converts those clues into definite directions.

Pattern: Direction with Conditions

Pattern

Key concept: Treat each conditional statement as a reversible operation - translate turns to +/- rotations (or swaps) and backtrack from the final condition to find the initial direction.

Practical rules

  • Translate directions to a numeric angle or to the compass labels (N, NE, E, SE, S, SW, W, NW).
  • Represent a turn as +90° (right) or -90° (left) or ±45° for intercardinal shifts; apply algebraic reversal to infer original direction.
  • When conditions include statements like “if P walks north and turns right he faces east”, treat that as an equation to solve for the unknown initial facing.
  • For multi-clause conditions, chain the inferences step-by-step and check consistency across clauses.

Step-by-Step Example

Question

A says: “If B walks north and then turns right, he faces East.” In which direction was B initially facing?

  1. North
  2. West
  3. South
  4. East

Solution

  1. Step 1: Translate the conditional into an operation

    The statement says: B walks north (i.e., he faces North while walking) and then turns right, after which he faces East.

  2. Step 2: Represent the turn algebraically

    Turning right = +90°. So: (Direction after walking north) + 90° = East.

  3. Step 3: Solve for the walking direction

    East corresponds to 90° (if North = 0°). Therefore walking direction + 90° = 90° → walking direction = 0° → North.

  4. Final Answer:

    North → Option A

  5. Quick Check:

    If B walks North and turns right, he faces East - consistent with the condition. ✅

Quick Variations

1. Conditions that require back-tracing multiple turns (e.g., “after two turns he faces west”).

2. Conditional comparative statements: “If P faces Q then R is to the left of P.”

3. Mixed time/position conditions: “In the morning his shadow fell left; after turning, the shadow was front.”

4. Symbolic conditions (e.g., A#B meaning north of) combined with directional turns.

Trick to Always Use

  • Step 1: Convert words to operations (walk north → face 0°; right → +90°, left → -90°).
  • Step 2: If the condition gives a final facing, write an equation and algebraically backtrack to the initial facing.
  • Step 3: For multiple conditions, chain equations and cross-check each clause for consistency; discard contradictory assumptions.

Summary

Summary

  • Translate each condition into a reversible directional operation (+90°, -90°, etc.).
  • Represent directions numerically or on a compass to simplify backtracking.
  • Chain multiple conditions step by step to find the original or final direction.
  • Verify your inference by forward-checking the condition to confirm consistency.

Example to remember:
If turning right from North leads to East, then the initial direction must be North.

Practice

(1/5)
1. A says: “If B walks north and then turns right, he faces East.” Which direction does B face immediately after the right turn?
easy
A. East
B. North
C. West
D. South

Solution

  1. Step 1: Identify given

    The statement says B walks north and then turns right, after which he faces East.

  2. Step 2: Apply the turn

    Walking north means facing North; turning right from North gives East.

  3. Step 3: Conclude

    So immediately after the right turn B faces East.

  4. Final Answer:

    East → Option A

  5. Quick Check:

    North → right = East ✅
Hint: Translate 'walk north' to facing North, then apply +90° for a right turn.
Common Mistakes: Treating the walking direction and final facing as unrelated.
2. A person is facing South. He turns left, then turns left again. Which direction is he facing now?
easy
A. South
B. North
C. East
D. West

Solution

  1. Step 1: Identify start orientation

    Initial facing = South.

  2. Step 2: Apply first left turn

    Left from South = East.

  3. Step 3: Apply second left turn

    Left from East = North.

  4. Final Answer:

    North → Option B

  5. Quick Check:

    Two successive lefts = 180° flip → South → North ✅
Hint: Two lefts (or two rights) = opposite direction.
Common Mistakes: Mixing left and right order or applying turns to wrong base direction.
3. E claims: “If F faces West and turns 90° anticlockwise, he faces South.” Is E’s claim correct?
easy
A. No
B. Only if in southern hemisphere
C. Yes
D. Cannot determine

Solution

  1. Step 1: Translate directions to angles

    West = 270° (taking North = 0° convention).

  2. Step 2: Apply anticlockwise rotation

    Anticlockwise 90° = subtract 90° → 270° - 90° = 180°.

  3. Step 3: Map back to compass

    180° corresponds to South, so the claim is correct.

  4. Final Answer:

    Yes → Option C

  5. Quick Check:

    West - 90° (ACW) = South ✅
Hint: Anticlockwise = subtract angle; clockwise = add angle (use North=0° mapping).
Common Mistakes: Using wrong sign for anticlockwise vs clockwise rotations.
4. G says: “If H faces North, turns right twice and then turns left, he will face East.” Is G’s statement true?
medium
A. Always true
B. True only if first right is 45°
C. False
D. Cannot determine

Solution

  1. Step 1: Start from North

    Initial facing = North.

  2. Step 2: Apply two right turns

    Right once: North → East. Right twice: East → South.

  3. Step 3: Apply final left turn

    Left from South → East.

  4. Final Answer:

    Always true → Option A

  5. Quick Check:

    N → R → R → L = East ✅
Hint: Two rights = 180°; then left = net +90° from start.
Common Mistakes: Miscounting the sequence of turns or assuming non-90° turns.
5. If a person says: “After walking East he turns left, walks, then turns left again and faces West,” which of the following initial facing directions before the first left-turn is possible?
medium
A. South
B. North
C. None of these
D. East

Solution

  1. Step 1: Interpret the statement

    The person walks East (so is facing East while walking), then turns left, walks, turns left again and finally faces West.

  2. Step 2: Apply the turns sequentially

    Start facing East. First left from East → North. Second left from North → West.

  3. Step 3: Verify final facing

    After the two left turns the person faces West - matches the statement. So initial facing while walking East was East.

  4. Final Answer:

    East → Option D

  5. Quick Check:

    East → left = North → left = West ✅
Hint: Track facing direction step-by-step; walking direction sets the start facing.
Common Mistakes: Assuming walking East means a different initial facing; forgetting turns are relative to current facing.

Mock Test

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