Scheduling, Routes and Network Logic Previous Year Questions (PYQs) for CAT: 33+ Solved Questions with Step-by-Step Solutions

Solve 33+ Scheduling, Routes and Network Logic previous year questions for CAT with answers and detailed solutions. Free sample questions below.

Chapter Roadmap: Scheduling, Routes and Network Logic

Chapter Journey: Scheduling, Routes and Network Logic

1. Route Maps, Walkways and Network Paths (Current Topic)

Focus: Decoding spatial networks, shortest paths, and movement constraints.
Weightage: High. Foundation for all network-based logical reasoning.

2. Time Slots, Queues and Ride Scheduling

Focus: Allocating limited resources across fixed time slots.
Weightage: High. Tests sequential logic and capacity constraints.

3. Year-Based Training and Publication Schedules

Focus: Sequencing events over years with multiple participants and gaps.
Weightage: Medium-High. Requires careful timeline mapping.

4. Firm Lifecycle and Funding Timelines

Focus: Overlapping intervals, start and end years, and cumulative sums.
Weightage: Medium. Tests interval logic and arithmetic.

Goal: By the end of this chapter, you will be able to instantly visualize any network or schedule, identify critical constraints, and solve complex multi-step reasoning problems with confidence.

The Hero Concept: Networks as Graphs of Nodes and Edges

The Core Model: Nodes and Edges

Every network problem, whether it involves stations, intersections, or gated community walkways, can be reduced to a Graph.

Nodes (Vertices): The specific points of interest (e.g., Stations, Intersections).
Edges (Links): The connections between nodes (e.g., Streets, Walkways). They often have weights (distance, time) or directions.

First Step in Any Problem:
1. Identify all Nodes.
2. List all direct Connections (Edges).
3. Note any Constraints (One-way? Blocked? Distance?).

Intuition: Think of the network as a social circle. Who knows whom directly? If A knows B, and B knows C, can A reach C? Yes, through B. This is the basis of all pathfinding.

Scheduling, Routes and Network Logic: Solved Questions with Step-by-Step Explanations (5 Problems)

Question 1 · Data Interpretation and Logical Reasoning MCQ

Common Description: Instructions [25 - 30]
A journal plans to publish 18 research papers, written by eight authors (A, B, C, D, E, F, G, and H) in four issues of the journal scheduled in January, April, July and October. Each of the research papers was written by exactly one of the eight authors. Five papers were scheduled in each of the first two issues, while four were scheduled in each of the last two issues. Every author wrote at least one paper and at most three papers. The total number of papers written by A, D, G and H was double the total number of papers written by the other four authors. Four of the authors were from India and two each were from Japan and China. Each author belonged to exactly one of the three areas — Manufacturing, Automation, and Logistics. Four of the authors were from the Logistics area and two were from the Automation area. As per the journal policy, none of the authors could have more than one paper in any issue of the journal.
The following facts are also known.
1. F, an Indian author from the Logistics area, wrote only one paper. It was scheduled in the October issue.
2. A was from the Automation area and did not have a paper scheduled in the October issue.
3. None of the Indian authors were from the Manufacturing area and none of the Japanese or Chinese authors were from the Automation area.
4. A and H were from different countries, but had their papers scheduled in exactly the same issues.
5. C and E, both Chinese authors from different areas, had the same number of papers scheduled. Further, E had papers scheduled in consecutive issues of the journal but C did not.
6. B, from the Logistics area, had a paper scheduled in the April issue of the journal.
7. B and G belonged to the same country. None of their papers were scheduled in the same issue of the journal.
8. D, a Japanese author from the Manufacturing area, did not have a paper scheduled in the July issue.
9. C and H belonged to different areas. Which of the following statement(s) MUST be true?
Statement A: Every issue had at least one paper by author(s) from each country.
Statement B: Every issue had at most two papers by author(s) from each area.

A.
Both the statements
B.
Only Statement B
C.
Only Statement A
D.
Neither of the statements

Correct Answer:

Step-by-Step Solution

Key idea: Universal Statement Validation. This puzzle requires evaluating two universal claims against all valid schedules derived from the common description.

Step 1: Recall Deduced Attributes.

Counts: A=3, D=3, G=3, H=3, B=1, C=2, E=2, F=1.

Countries: Ind(A,B,F,G), Jap(D,H), Chi(C,E).

Areas: Auto(A,G), Mfg(C,D), Log(B,E,F,H).

Step 2: Recall Placements.

A, H in ${J an, A p r, J u l}$ . D in ${J an, A p r, O c t}$ . G in ${J an, J u l, O c t}$ .

B in Apr only. F in Oct only.

C and E fill the remaining 1 slot per issue (4 slots total, 2 each).

Step 3: Evaluate Statement A.

Claim: Every issue has at least one paper from each country.

Chinese: C and E together fill exactly 1 slot per issue. So every issue has exactly 1 Chi paper. Check.

Indian: A covers Jan, Apr, Jul. G covers Jan, Jul, Oct. B covers Apr. F covers Oct.

Jan: A, G (Ind). Apr: A, B (Ind). Jul: A, G (Ind). Oct: G, F (Ind). Every issue has Ind. Check.

Japanese: D covers Jan, Apr, Oct. H covers Jan, Apr, Jul.

Jan: D, H. Apr: D, H. Jul: H. Oct: D. Every issue has Jap. Check.

Statement A is TRUE in all valid schedules.

Step 4: Evaluate Statement B.

Claim: Every issue has at most 2 papers from each area.

Logistics authors: B, E, F, H.

April has H (Log) and B (Log) for sure.

If E is placed in April (valid: E is consecutive, e.g., Apr-Jul), April has H, B, E = 3 Logistics papers.

This violates the at-most-2 claim.

Statement B is NOT necessarily true.

Step 5: Conclusion.

Only Statement A must be true.

Answer: C

Question 2 · Data Interpretation and Logical Reasoning MCQ

Common Description: Instructions [30 - 33]
The above is a schematic diagram of walkways (indicated by all the straight-lines) and lakes (3 of them, each in the shape of rectangles - shaded in the diagram) of a gated area. Different points on the walkway are indicated by letters (A through P) with distances being OP = 150 m, ON = MN = 300 m, ML = 400 m, EL = 200 m, DE = 400 m.

The following additional information about the facilities in the area is known.
1. The only entry/exit point is at C.
2. There are many residences within the gated area; all of them are located on the path AH and ML with four of them being at A, H, M, and L.
3. The post office is located at P and the bank is located at B. One resident whose house is located at L, needs to visit the post office as well as the bank. What is the minimum distance (in m) he has to walk starting from his residence and returning to his residence after visiting both the post office and the bank?

A.
2700
B.
3200
C.
3000
D.
3400

Correct Answer:

Step-by-Step Solution

Key idea: Shortest path (TSP) on a grid with diagonal walkways.

Step 1: Map the grid dimensions.

Horizontal widths: P-O = 150, O-N = 300, N-M = 300.

Vertical heights: M-L = 400, L-E = 200, E-D = 400.

Diagonals available: I-G (connects Row 3 and Row 2, dx=150, dy=200 $\to$ length 250). O-K (connects Row 4 and Row 3, dx=300, dy=400 $\to$ length 500).

Step 2: Identify key nodes. Residence L, Post Office P, Bank B.

Step 3: Calculate shortest path L $\to$ P.

Manhattan distance = 750 + 400 = 1150.

Using diagonal O-K (saves 200): L $\to$ K (300) $\to$ O (500) $\to$ P (150) = 950.

Step 4: Calculate shortest path P $\to$ B.

Manhattan distance = 150 + 1000 = 1150.

Using diagonal I-G (saves 100): P $\to$ I (400) $\to$ G (250) $\to$ B (400) = 1050.

Step 5: Calculate shortest path B $\to$ L.

Manhattan distance = 600 + 600 = 1200. No diagonals help here.

Path: B $\to$ G (400) $\to$ F (300) $\to$ E (300) $\to$ L (200) = 1200.

Step 6: Total minimum distance = 950 + 1050 + 1200 = 3200 m.

Answer: B

Question 3 · Data Interpretation and Logical Reasoning NAT

Common Description: Instructions [30 - 33]
The above is a schematic diagram of walkways (indicated by all the straight-lines) and lakes (3 of them, each in the shape of rectangles - shaded in the diagram) of a gated area. Different points on the walkway are indicated by letters (A through P) with distances being OP = 150 m, ON = MN = 300 m, ML = 400 m, EL = 200 m, DE = 400 m.

The following additional information about the facilities in the area is known.
1. The only entry/exit point is at C.
2. There are many residences within the gated area; all of them are located on the path AH and ML with four of them being at A, H, M, and L.
3. The post office is located at P and the bank is located at B. One resident takes a walk within the gated area starting from A and returning to A without going through any point (other than A) more than once. What is the maximum distance (in m) she can walk in this way?

Correct Answer:

5100

Step-by-Step Solution

Key idea: Longest Simple Cycle on a weighted grid graph. This is a network tracing question, recognisable by asking for the "maximum distance" to return to start without repeating points.

Step 1: Map the network topology and edge weights. Horizontal edges: AB=150, BC=300, CD=300; GH=150, GF=300, FE=200; IJ=150, JK=300, KL=400; PO=150, ON=300, NM=300. Vertical edges: AH=400, BG=400, CF=400, DE=400; HI=200, GJ=200, FK=200, EL=200; IP=400, JO=400, KN=400, LM=400. Diagonal edges: IG and OK. Note: $I G = 15 0^{2} + 20 0^{2} = 250$ . Path $I H + H G = 200 + 150 = 350$ . Since $350 > 250$ , diagonals are always shorter. To MAXIMIZE distance, AVOID diagonals entirely.

Step 2: Identify forced edges. Nodes with degree 2 in the grid subgraph MUST use both incident edges in any cycle. Corners A, D, M, P have degree 2. Forced edges: AB, AH, CD, DE, NM, LM, PO, PI.

Step 3: Construct the maximal cycle. The optimal path traces the outer boundary and weaves through internal nodes without using diagonals.

Valid Maximal Cycle Route: A $\to$ H $\to$ I $\to$ P $\to$ O $\to$ N $\to$ M $\to$ L $\to$ K $\to$ J $\to$ G $\to$ F $\to$ E $\to$ D $\to$ C $\to$ B $\to$ A.

Step 4: Sum the distances. AH(400) + HI(200) + IP(400) + PO(150) + ON(300) + NM(300) + ML(400) + LK(400) + KJ(300) + JG(200) + GF(300) + FE(200) + ED(400) + DC(300) + CB(300) + BA(150) = 5100.

Answer: 5100

Question 4 · Data Interpretation and Logical Reasoning MCQ

Common Description: Instructions [25 - 29]
The figure below shows a network with three parallel roads represented by horizontal lines R-A, R-B, and R-C and another three parallel roads represented by vertical lines V1, V2, and V3. The figure also shows the distance (in km) between two adjacent intersections. Six ATMs are placed at six of the nine road intersections. Each ATM has a distinct integer cash requirement (in Rs. Lakhs), and the numbers at the end of each line in the figure indicate the total cash requirements of all ATMs placed on the corresponding road. For example, the total cash requirement of the ATM(s) placed on road R-A is Rs. 22 Lakhs.

The following additional information is known.
1. The ATMs with the minimum and maximum cash requirements of Rs. 7 Lakhs and Rs. 15 Lakhs are placed on the same road.
2. The road distance between the ATM with the second highest cash requirement and the ATM located at the intersection of R-C and V3 is 12 km. What best can be said about the road distance (in km) between the ATMs having the second highest and the second lowest cash requirements?

A.
4 km
B.
7 km
C.
5 km
D.
Either 4 km or 7 km

Correct Answer:

Step-by-Step Solution

Key idea: Integer partitioning on a grid with row/column sum constraints combined with distance-based positional clues.

Step 1: Determine the set of 6 distinct ATM cash values. Min = 7, Max = 15. Sum of all ATMs = row sums = $22 + 20 + 20 = 62$ .

Sum of integers from 7 to 15 inclusive = 99. We need 6 distinct values summing to 62, so we exclude 3 values summing to 37.

The only valid excluded triple from ${8..14}$ that leaves a workable set is ${10, 13, 14}$ , giving the ATM set $S_{1} = {7, 8, 9, 11, 12, 15}$ .

Step 2: Place 7 and 15. Fact 1 says they are on the same road. Only R-A (sum 22) can accommodate $7 + 15 = 22$ exactly. So R-A contains exactly ${7, 15}$ .

Step 3: Test valid grid configurations.

Configuration 1: 15 is at (R-A, V1) and 7 is at (R-A, V3). To satisfy column sums (V1=15, V2=21, V3=26), V1 gets only ${15}$ . V3 gets ${7, 8, 11}$ and V2 gets ${9, 12}$ . To make row sums 20 for R-B and R-C, we pair 12 with 8, and 9 with 11. Fact 2 requires the distance between 2nd highest (12) and R-C, V3 to be 12 km. This forces 12 to be at (R-B, V2) and R-C, V3 to be 11. The 2nd lowest is 8 (at R-B, V3). The distance between 12 and 8 is 7 km.

Configuration 2: 7 is at (R-A, V1) and 15 is at (R-A, V3). V1 gets ${7, 8}$ , V3 gets ${15, 11}$ , V2 gets ${9, 12}$ . Row pairing forces 12 and 8 to be in the same row. Fact 2 again forces 12 to (R-B, V2) and R-C, V3 to be 11. The 2nd lowest is 8 (at R-B, V1). The distance between 12 and 8 is 4 km.

Step 4: Conclusion. Both configurations satisfy all conditions perfectly. The distance is either 4 km or 7 km.

Answer: D

Question 5 · Data Interpretation and Logical Reasoning MCQ

Common Description: Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur are four musicians. Each of them started and completed their training as students under each of three Gurus — Pandit Meghnath, Ustad Samiran, and Acharya Raghunath between 2013 and 2024, including both the years. Each Guru trains any student for consecutive years only, for a span of 2, 3, or 4 years, with each Guru having a different span. During some of these years, a student may not have trained under these Gurus; however, they never trained under multiple Gurus in the same year. In none of these years, any of these Gurus trained more than two of these students at the same time. When two students train under the same Guru at the same time, they are referred to as Gurubhai, irrespective of their gender.
The following additional facts are known.
1. Ustad Samiran never trained more than one of these students in the same year.
2. Acharya Raghunath did not train any of these students during 2015-2018, as well as during 2021-24.
3. Ananya and Devendra were never Gurubhai; neither were Bhaskar and Charu. All other pairs of musicians were Gurubhai for exactly 2 years.
4. In 2013, Ananya and Bhaskar started their trainings under Pandit Meghnath and under Ustad Samiran, respectively. In which of the following years were Ananya and Bhaskar Gurubhai?

A.
2020
B.
2018
C.
2021
D.
2014

Correct Answer:

Step-by-Step Solution

Key idea: Temporal Scheduling and Constraint Satisfaction. This is a timeline scheduling question, recognisable by entities training under Gurus for specific year spans and asking for overlap years (Gurubhai).

Step 1: Map the constraints. 4 students (A, B, C, D), 3 Gurus (PM, US, AR). Spans are 2, 3, 4 years. Each Guru has a different span. US never trains >1 student per year.

Step 2: Deduce timelines. Ananya (A) starts PM in 2013. Bhaskar (B) starts US in 2013. Based on the non-overlap rules and spans, the deduced timelines are: Ananya: PM(2013-2016), AR(2019-2020), US(2022-2024). Bhaskar: US(2013-2015), AR(2019-2020), PM(2021-2024).

Step 3: Identify overlaps. They are Gurubhai under AR (2019-2020) for 2 years. They do not overlap under PM or US because US capacity is 1, and their PM blocks are disjoint.

Step 4: Match with options. The overlap years are 2019 and 2020. Option A is 2020.

Answer: A

Trap: Confusing the start years or miscalculating the span durations, leading to incorrect overlap years.

Scheduling, Routes and Network Logic Previous Year Questions (PYQs) for CAT: 33+ Solved Questions with Step-by-Step Solutions

Chapter Roadmap: Scheduling, Routes and Network Logic

Chapter Journey: Scheduling, Routes and Network Logic

1. Route Maps, Walkways and Network Paths (Current Topic)

2. Time Slots, Queues and Ride Scheduling

3. Year-Based Training and Publication Schedules

4. Firm Lifecycle and Funding Timelines

The Hero Concept: Networks as Graphs of Nodes and Edges

The Core Model: Nodes and Edges

Scheduling, Routes and Network Logic: Solved Questions with Step-by-Step Explanations (5 Problems)

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

More previous year questions (pyqs) in this unit

A question from this chapter

Login to view the complete previous-year questions and solutions

Personalised first. High quality throughout.

Built around you, not around a syllabus PDF

Revision that hits your weak spots

Questions calibrated to the real exam

Notes written for recall, not for volume

One place for everything

Honest progress

Unlock the whole course