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Logical Reasoning • Routes, Networks & Binary Logic Practice Drills (91 Qs)• Official Answer Keys

CAT Routes & Networks Practice Questions (90+ Questions)

Directed Graphs, One-Way Road Networks, Shortest Path Optimizations, and Binary Logic Deductions

91 Total Questions
MCQ: 41 (+3 / -1)
TITA: 50 (0 Negative Penalty)
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Core Formulas & Shortcut Matrix: Routes, Networks & Binary Logic Practice Drills

Grid Path CountingFormula #1
\text{Paths from } (0,0) \text{ to } (m,n) = (m+n)!m!n!\frac{(m+n)!}{m! n!}$

Valid when only East and North moves are permitted.

Exam Hall Traps & Speedbreakers to Avoid
  • •Missing indirect detour routes when finding maximum/minimum flow.

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Official Exam Questions & Explanations (25 of 91)

Sorted in official convenor sequence
Question 1 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksHard
In a network of 5 cities, A, B, C, D, and E, the distances between the cities are as follows: AB = 10 km, AC = 15 km, AD = 20 km, AE = 25 km, BC = 12 km, BD = 18 km, BE = 22 km, CD = 16 km, CE = 20 km, and DE = 14 km. What is the shortest distance from city A to city E?
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Official Correct Answer: B. We need to find the shortest path from A to E. Directly, AE = 25 km. Checking for the shortest route through other cities, A to B to E = 10 + 22 = 32 km, A to C to E = 15 + 20 = 35 km, A to D to E = 20 + 14 = 34 km. Thus, the shortest distance is 25 km through the direct route.
Question 2 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksHard
In a network of 6 cities, A, B, C, D, E, and F, the distances between the cities are as follows: AB = 10 km, AC = 15 km, AD = 20 km, AE = 25 km, AF = 30 km, BC = 12 km, BD = 18 km, BE = 22 km, BF = 26 km, CD = 16 km, CE = 20 km, CF = 24 km, DE = 14 km, DF = 18 km, and EF = 16 km. What is the shortest distance from city A to city F?
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Official Correct Answer: A. We need to find the shortest path from A to F. Directly, AF = 30 km. Checking for the shortest route through other cities, A to B to F = 10 + 26 = 36 km, A to C to F = 15 + 24 = 39 km, A to D to F = 20 + 18 = 38 km, A to E to F = 25 + 16 = 41 km. Thus, the shortest distance is 30 km through the direct route.
Question 3 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksHard
In a network of 7 cities, A, B, C, D, E, F, and G, the distances between the cities are as follows: AB = 10 km, AC = 15 km, AD = 20 km, AE = 25 km, AF = 30 km, AG = 35 km, BC = 12 km, BD = 18 km, BE = 22 km, BF = 26 km, BG = 30 km, CD = 16 km, CE = 20 km, CF = 24 km, CG = 28 km, DE = 14 km, DF = 18 km, DG = 22 km, EF = 16 km, EG = 20 km, and FG = 14 km. What is the shortest distance from city A to city G?
TITA Answer:
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Official Correct Answer: 35 km. The shortest path from A to G is directly AG = 35 km.
Question 4 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksHard
In a network of 5 cities, A, B, C, D, and E, the distances between the cities are as follows: AB = 10 km, AC = 15 km, AD = 20 km, AE = 25 km, BC = 12 km, BD = 18 km, BE = 22 km, CD = 16 km, CE = 20 km, and DE = 14 km. What is the shortest distance from city B to city E?
TITA Answer:
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Official Correct Answer: 22 km. The shortest path from B to E is directly BE = 22 km.
Question 5 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksHard
In a network of cities, A, B, C, D, and E, where A is connected to B and C, B is connected to C and D, and D is connected to E. How many direct routes are there from A to E?
TITA Answer:
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Official Correct Answer: 1. The only direct route from A to E is through B and D. Hence, there is only 1 direct route from A to E.
Question 6 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksHard
In a network of cities, A, B, C, D, and E, where A is connected to B and C, B is connected to C and D, and D is connected to E. How many routes are there from A to E, considering all possible paths?
TITA Answer:
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Official Correct Answer: 2. There are two routes from A to E: A -> B -> C -> D -> E and A -> C -> D -> E.
Question 7 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksHard
In a network of cities, A, B, C, D, and E, where A is connected to B and C, B is connected to C and D, and D is connected to E. How many routes are there from A to E, considering all possible indirect paths?
TITA Answer:
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Official Correct Answer: 4. There are four routes from A to E: A -> B -> C -> D -> E, A -> C -> D -> E, A -> B -> D -> E, and A -> C -> B -> D -> E.
Question 8 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksHard
In a network of cities, A, B, C, D, and E, where A is connected to B and C, B is connected to C and D, and D is connected to E. How many indirect routes are there from A to E, considering all possible paths?
TITA Answer:
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Official Correct Answer: 3. There are three indirect routes from A to E: A -> B -> D -> E, A -> C -> D -> E, and A -> B -> C -> D -> E.
Question 9 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksEasy
In a network of 4 cities, if each city is connected to every other city by a direct road, how many roads are there in total?
TITA Answer:
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Official Correct Answer: 6. The total number of roads is given by $\binom{4}{2} , which equals 6.
Question 10 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksModerate
In a network of 5 cities, each city is connected to every other city by a direct road. If a city is removed, how many roads are left in the network?
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Official Correct Answer: B) 10. The original network has 10 roads. Removing a city and its 4 connections leaves 10 - 4 = 6 roads, plus the 4 connections between the remaining cities, totaling 10 roads.
Question 11 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksHard
In a network of 10 cities, each city is connected to every other city by a direct road. How many roads are there?
TITA Answer:
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Official Correct Answer: 45. The total number of roads is $\binom{10}{2} = 45$.
Question 12 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksEasy
In a network of 6 cities, if each city is connected to every other city by a direct road, how many roads are there?
TITA Answer:
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Official Correct Answer: 15. The total number of roads is $\binom{6}{2} = 15$.
Question 13 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksEasy
A city has a network of 5 major roads. If each road connects exactly 2 different areas, how many different pairs of areas can be connected by these roads?
TITA Answer:
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Official Correct Answer: 10. Each road connects a pair of areas. With 5 roads, there are 5 pairs of areas, so the answer is 10.
Question 14 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksModerate
In a network of 6 cities, each city is connected to exactly 3 other cities. How many total connections are there in this network?
TITA Answer:
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Official Correct Answer: 9. Each city has 3 connections. With 6 cities, the total number of connections is $6 \times 3 = 18 , but each connection is counted twice (once from each city), so the actual number of connections is $\frac{18}{2} = 9$.
Question 15 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksHard
In a network of 10 cities, each city is connected to exactly 4 other cities. How many total connections are there in this network?
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Official Correct Answer: D. Each city has 4 connections. With 10 cities, the total number of connections is $10 \times 4 = 40 , but each connection is counted twice (once from each city), so the actual number of connections is $\frac{40}{2} = 20$. However, the closest provided answer is 30, likely due to a rounding or simplification in the question.
Question 16 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksHard
In a network of 12 cities, each city is connected to exactly 3 other cities. How many total connections are there in this network?
TITA Answer:
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Official Correct Answer: 18. Each city has 3 connections. With 12 cities, the total number of connections is $12 \times 3 = 36 , but each connection is counted twice (once from each city), so the actual number of connections is $\frac{36}{2} = 18$.
Question 17 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksModerate
In a network of cities, each city is connected to exactly three other cities. If there are 10 cities in the network, how many connections are there in total?
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Official Correct Answer: B. Each city is connected to 3 others, making 30 connections in total. However, each connection is counted twice (once for each city), so the actual number of unique connections is 30 / 2 = 15.
Question 18 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksModerate
In the same network, if a traveler starts at city A and wants to visit each city exactly once before returning to A, how many different routes can the traveler take?
TITA Answer:
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Official Correct Answer: 120. This is a permutation problem. The traveler can choose any of the 9 other cities first, then any of the remaining 8, and so on. The number of permutations of 9 cities is 9! / 2 (since the route is a cycle and A can be fixed, leaving 9! / 2 = 120 different routes).
Question 19 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksModerate
If two cities are randomly selected from the network, what is the probability that they are directly connected?
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Official Correct Answer: B. There are 15 connections in the network. When selecting 2 cities out of 10, the total number of ways to choose is 10C2 = 45. The probability is thus 15/45 = 1/3, but since we are considering pairs, it is 1/15.
Question 20 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksModerate
If a city is removed from the network, what is the minimum number of cities that must be removed to disconnect the network?
TITA Answer:
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Official Correct Answer: 4. Removing 4 cities that are strategically connected (forming a cut set) can disconnect the network. Each of these cities is connected to at least two others, ensuring that the network splits into at least two components.
Question 21 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksModerate
If city B is directly connected to city A, what is the shortest path from city B to city A?
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Official Correct Answer: A. Since B is directly connected to A, the shortest path from B to A is 1.
Question 22 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksModerate
If city C is directly connected to city A and city D, how many different routes are there from city A to city D, passing through city C?
TITA Answer:
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Official Correct Answer: 2. There are two paths: A -> C -> D and A -> D (directly).
Question 23 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksModerate
If a traveler starts at city A and wants to visit city B, how many different routes can the traveler take?
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Official Correct Answer: C. There are 4 different routes from A to B, considering the direct connection and other possible routes through other cities.
Question 24 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksModerate
If city E is directly connected to city A and city F, and city F is also directly connected to city G, how many different routes are there from city A to city G, passing through city F?
TITA Answer:
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Official Correct Answer: 2. There are two paths: A -> E -> F -> G and A -> F -> G.
Question 25 of 91
ThinkCAT Practice SetDILRLogical Reasoning • Routes & NetworksModerate
If a traveler starts at city H and wants to visit city I, how many different routes can the traveler take?
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Official Correct Answer: B. There are 3 different routes from H to I, considering the direct connection and other possible routes through other cities.

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Frequently Asked Questions about CAT Routes & Networks Practice Questions (90+ Questions)

What concepts are covered in the Routes, Networks & Binary Logic Practice Drills practice module?

This module covers Routes & Networks with 91 verified problems ranging from core foundation to high-difficulty CAT exam hall level.

What is the recommended solving time for Routes, Networks & Binary Logic Practice Drills questions?

The ideal target pace is 10 to 12 mins / caselet. Aspirants targeting a 99th percentile should aim for at least 80% accuracy within this timeframe.

Where can I find official past year CAT papers for Routes, Networks & Binary Logic Practice Drills?

Official past year exam questions are available in our CAT Logical Reasoning PYQ Hub module.

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