Data Interpretation & Logical Reasoning / Analytical reasoning

Networks, Routes, Scheduling & Optimization

Connected paths, project order, time slots, and best feasible outcomes.

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Start with the basics

Networks, Routes, Scheduling & Optimization, explained simply

A network connects places or tasks. A route follows connections; a schedule puts tasks in time order.

Try a small example

A path from A to B takes 4 minutes and B to C takes 3. If there is no waiting, how long does A to B to C take?

Show the steps

The route uses both path segments.
Add their times: 4 + 3.
The journey takes 7 minutes.

Remember: The route with the fewest connections is not always the quickest.

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BEGINNER

Core idea

A network is a picture of places or tasks linked by lines. A route follows those links. A schedule places tasks into time slots. Some tasks can start only after others finish. The shortest or fastest answer must still obey every rule.

Exam focus

CAT: Data Interpretation and Logical Reasoning

Solve linked sets, not just isolated calculations. Select sets by clarity of constraints; build one representation for all questions.

Check your understanding

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

Routes and Networks

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

Review the note

Check your answer

Represent places as vertices and allowed journeys as edges. Distinguish the shortest route from the route with the fewest edges.

Worked example: A-B costs 2, B-C costs 3 and A-C costs 8. The two-edge route A-B-C costs 5 and is cheaper than the direct edge.

Scheduling

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

Review the note

Check your answer

A schedule must respect prerequisites and resource conflicts. Earliest finish for a dependent task uses the latest prerequisite finish, not their sum when tasks run in parallel.

Worked example: A takes 2 hours and B takes 3, starting together. C takes 4 hours and requires both. C starts at hour 3 and finishes at hour 7.

Optimization

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

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Check your answer

A good optimum needs both a bound and a construction that achieves it. One workable answer proves feasibility, not optimality.

Worked example: Two machines can each process 4 jobs per hour. Ten jobs need at least 10/8 hours in a divisible-work model. If jobs are indivisible and each lasts 15 minutes, schedule five per machine to achieve 75 minutes.

Practice questions

Bharatiya Pathshala

Opening preparation notes...

BEGINNER

Networks, Routes, Scheduling & Optimization: visual worked lesson

Core idea

A network connects places or tasks. A route follows connections; a schedule puts tasks in time order.

Solving method

Draw directed edges for dependencies and label route costs separately. Earliest finish uses the latest predecessor finish, not the sum of independent branches.

Worked example

A path from A to B takes 4 minutes and B to C takes 3. If there is no waiting, how long does A to B to C take? 1. The route uses both path segments. 2. Add their times: 4 + 3. 3. The journey takes 7 minutes.

Read the diagram

The circles are locations and the directed links are the route being followed. Add the link times to obtain 7 minutes. If there is waiting, a transfer time or a prerequisite, include it separately. This drawing demonstrates one route; it does not claim that no alternative route exists.

Exam-style application

Task A takes 3 hours. B takes 4 after A; C takes 2 after A. D takes 5 after both B and C. A finishes at 3, B at 7, C at 5, so D starts at max(7,5)=7 and ends at 12. Critical path A-B-D has length 12. Speeding up C by one hour does not improve project completion because B still controls D's start.

Common mistakes

The route with the fewest connections is not always the quickest. A shorter individual task need not shorten the whole schedule. Check resource limits before assuming parallel execution.

A route has links with travel times. No waiting is included in this route. — A route has links with travel times

No waiting is included in this route. — A route has links with travel times

Formulas to remember

Route time = travel times + waiting times

Source record: Bharatiya Pathshala — original illustrated lessons.

Networks, Routes, Scheduling & Optimization, explained simply

Try a small example

Core idea

CAT: Data Interpretation and Logical Reasoning

Check your understanding

Routes and Networks

Scheduling

Optimization

Networks, Routes, Scheduling & Optimization, explained simply

Try a small example

Networks, Routes, Scheduling & Optimization: visual worked lesson

Core idea

Solving method

Worked example

Read the diagram

Exam-style application

Common mistakes

Formulas to remember

Core idea

Steps

Worked example

Common mistake

Optimization

Worked example

Application and strategy

Worked application

Common traps and strategy

CAT: Data Interpretation and Logical Reasoning

Check your understanding

Routes and Networks

Scheduling

Optimization

Networks, Routes, Scheduling & Optimization: visual worked lesson

Core idea

Solving method

Worked example

Read the diagram

Exam-style application

Common mistakes

Formulas to remember

Steps

Worked example

Common mistake

Optimization

Worked example

Application and strategy

Worked application

Common traps and strategy