Routes & Network - CAT MCQ

The possible routes are as follows:

A - B - C - D - E - F - A = 15 + 22 + 25 + 28 + 21 + 24 = 135 km.
Since there is only one route which covers all villages and pass through a village only once.
Hence, 135 km is the correct answer.

The possible routes are as follows:

TQSRP

TPRSQ

TQPRS

TPQSR

Here, four such routes are possible.
Hence, four is the correct answer.

On analyzing the options:
(1)

Here, there are six sites, one site with one route, four sites with two routes and one site with three routes.
(2)

Here, there are six sites, one site with one route, two sites with two routes and three sites with three routes
(3)

Here, there are six sites, one site with one route, two sites with two routes and three sites with three routes.
(4)

Here, there are six sites, one site with one route, two sites with two routes and three sites with three routes.
Hence, option 1 is the correct answer.

Except for option(1), every map shows four 3-road junctions and two 2-road junctions while option(1) shows all junctions have 3-road junctions.
Hence the correct answer is an option(1) i.e.,

For this question, we can take all points one by one.

Such route started from Point A: Yes it exists, route ACDEBDAB, etc.

Such route started from Point B: Yes it exist , route BADEBDCA, etc.

Such route started from Point C: No it does not exist.

Such route started from Point D: No it does not exist.

Such route started from Point E: No it does not exist.

So, such route is started only from two points i.e., A and B.

Hence, the correct answer is option(3)i.e. Two.

1. There are two one-way roads between P and Q.
2. There are three one-way roads between Q and R.

3. There is only one two-way road between R and T.

4. S and T are connected by two two-way roads.
5. S and U are connected by two one-way road.

If a person has to visit town S, starting from two Q. There are six possible ways.

Hence, the correct answer is 6.

The movement of symbols is as follows:

The symbol at position 1 will duplicate and move at position 9 and 6. The symbol at position 9 will duplicate and place at 4 and 3. The symbol at position 3 will move at position 5. The symbol at position 5 will move at position 7. The symbol at position 7 will move at position 1. The final figure will be as follows: 

The possible routes are as follows:

T - P - R - Q - S - T = 22 + 15 + 26 + 19 + 20 = 102 km
T - P - Q - R - S - T = 22 + 24 + 26 + 17 + 20 =  109 km
T - S - Q - R - P - T = 20 + 19 + 26 +15 + 22 = 102 km
T - S - R - Q - P - T =  20 + 17 + 26 + 24 + 22 =  109 km
Hence, 109 km is the correct answer.

On analyzing the options:
(1)

Here, there six stops, one stop with one route, two stops with two routes, three stops with three routes.
(2)

Here, there six stops, one stop with one route, two stops with two routes, three stops with three routes.
(3)

Here, there six stops, one stop with one route, two stops with two routes, three stops with three routes.
(4)

Here, there six stops, one stop with one route, four stops with two routes, one stop with three routes.

In each of the given options figure 4 is not the same as others.

Hence, option 4 is the correct answer.

There are six possibilities to visit clients and return to pali.

(1) Pali - Neli - Seli - Teli - Pali

Distance = 31 Km + 26 Km + 18 Km + 20 Km = 95 Km

(2) Pali - Neli - Teli - Seli - Pali

Distance = 31 Km + 16 Km + 18 Km + 22 Km = 87 Km

(3) Pali - Teli - Neli - Seli - Pali

Distance = 20 Km + 16 Km + 26 Km + 22 Km = 84 Km

(4) Pali - Teli - Seli - Neli - Pali

Distance = 20 Km + 18 Km + 26 Km + 31 Km = 95 Km

(5) Pali - Seli - Neli - Teli - Pali

Distance = 22 Km + 26 Km + 16 Km + 20 Km = 84 Km

(6) Pali - Seli - Teli - Neli - Pali

Distance = 22 Km + 18 Km + 16 Km + 31 Km = 87 Km

So, the minimum distance to visit clients and return to pali is 84 Km.

Hence, the correct answer is option(1) i.e., 84 Km.