Data Interpretation & Logical Reasoning / Short-form reasoning

Direction Sense

Direction Sense: concepts, worked examples and practice.

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Start with the basics

Direction Sense, explained simply

Direction problems track movement on a map. North is opposite south; east is opposite west.

Try a small example

Walk 3 metres east and then 3 metres west. Where are you relative to the start?

Show the steps

The eastward move adds 3 metres horizontally.
The westward move cancels that displacement.
You return to the start, although you walked 6 metres.

Remember: Distance travelled and displacement from the starting point are different.

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Turns and Displacement

Use a north-east coordinate grid. Distance travelled is the sum of path lengths; displacement is the straight-line change from start to finish.

Worked example

Walk 3 km east then 4 km north. Distance travelled is 7 km, but displacement is sqrt(3^2+4^2)=5 km towards the northeast.

Exam focus

MAT: Intelligence and Critical Reasoning

Use diagrams for relationships and distinguish logical necessity from everyday plausibility.

CMAT: Logical Reasoning

Translate statements into diagrams or simple conditions. Check whether a conclusion is necessary rather than merely possible.

NMAT: Logical Reasoning

Test assumptions and deductions, then use small structured cases for puzzles and input-output rules.

SNAP: Analytical and Logical Reasoning

Use compact diagrams, clear direction conventions and quick elimination. Skip long uncertain branches and return later.

Check your understanding

Explain the idea in your own words before opening the answer. Then apply it to the example.

Turns and Displacement

Explain the main rule in turns and displacement, then apply it to a small example. State the assumption that makes your reasoning valid.

Review the note

Check your answer

Use a north-east coordinate grid. Distance travelled is the sum of path lengths; displacement is the straight-line change from start to finish.

Worked example: Walk 3 km east then 4 km north. Distance travelled is 7 km, but displacement is sqrt(3^2+4^2)=5 km towards the northeast.

Relative Directions

Explain the main rule in relative directions, then apply it to a small example. State the assumption that makes your reasoning valid.

Review the note

Check your answer

Fix a common reference point and convert each location into coordinates. Someone's facing direction is different from where they are located.

Worked example: B is 4 km east of A; C is 3 km north of B. Relative to A, C is northeast. Relative to C, A is southwest.

Practice questions

Bharatiya Pathshala

Opening preparation notes...

BEGINNER

Direction Sense: visual worked lesson

Core idea

Direction problems track movement on a map. North is opposite south; east is opposite west.

Solving method

Set east as positive x and north as positive y. Record each movement as a vector; turns change facing, not position.

Worked example

Walk 3 metres east and then 3 metres west. Where are you relative to the start? 1. The eastward move adds 3 metres horizontally. 2. The westward move cancels that displacement. 3. You return to the start, although you walked 6 metres.

Read the diagram

The upper arrow goes east and the lower arrow returns west to the same starting location. Add travelled lengths to obtain 6 metres; subtract opposite signed displacements to obtain zero. The curved arrows distinguish the two moves schematically, rather than representing a curved path on the ground.

Exam-style application

A person walks 6 km north, turns right and walks 8 km, then turns right and walks 3 km. Position=(8,3), facing south. Displacement from the start=sqrt(8^2+3^2)=sqrt(73) km towards the north-east. Total distance walked=17 km. To return directly, travel south-west along vector (-8,-3).

Common mistakes

Distance travelled and displacement from the starting point are different. The final facing direction, direction from the start and total distance are three different answers.

Distance travelled differs from displacement. Total distance = 6 m; final displacement = 0 m. Arrows show travel order. — Distance travelled differs from displacement

Total distance = 6 m; final displacement = 0 m. Arrows show travel order. — Distance travelled differs from displacement

Formulas to remember

Distance = sum of travelled lengths

Displacement = final position − initial position

Source record: Bharatiya Pathshala — original illustrated lessons.

Direction Sense, explained simply

Try a small example

Turns and Displacement

Worked example

MAT: Intelligence and Critical Reasoning

CMAT: Logical Reasoning

NMAT: Logical Reasoning

SNAP: Analytical and Logical Reasoning

Check your understanding

Turns and Displacement

Relative Directions

Direction Sense, explained simply

Try a small example

Direction Sense: visual worked lesson

Core idea

Solving method

Worked example

Read the diagram

Exam-style application

Common mistakes

Formulas to remember

Turns and Displacement

Worked example

Relative Directions

Worked example

Application and strategy

Worked application

Common traps and strategy

MAT: Intelligence and Critical Reasoning

CMAT: Logical Reasoning

NMAT: Logical Reasoning

SNAP: Analytical and Logical Reasoning

Check your understanding

Turns and Displacement

Relative Directions

Direction Sense: visual worked lesson

Core idea

Solving method

Worked example

Read the diagram

Exam-style application

Common mistakes

Formulas to remember

Relative Directions

Worked example

Application and strategy

Worked application

Common traps and strategy