Logical Reasoning

Grids

Hard

Figure for CAT 2024 DILR question 6 (Logical Reasoning)

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.

The only entry/exit point is at C.
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.
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?

3200

3000

2700

✅ Correct Option: 1

Firstly, let's calculate the length of the paths in this question:-

KN = ML = 400m

and. ON = 300m

Using phythagorus theorum,

KO = 500m

Similairly,

HJ = OP = 150m

GJ = EL = 200m

HG = 250m

The shortest path is L-K-O-P-I-G-B-C-F-E-L.

Hence the minimum distance is LK+KO+OP+PI+IG+GB+BC+CF+FE+EL=

300+500+150+400+250+400+300+400+300+200= 3200 m.

Question 7

One person enters the gated area and decides to walk as much as possible before leaving the area without walking along any path more than once and always walking next to one of the lakes. Note that he may cross a point multiple times. How much distance (in m) will he walk within the gated area?

Question 8

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?

$\square$

Question 9

Visitors coming for morning walks are allowed to enter as long as they do not pass by any of the residences and do not cross any point (except C) more than once. What is the maximum distance (in m) that such a visitor can walk within the gated area?

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?

Solution

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