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CAT 2024 Slot 2 — DILR Question 1

Mixed PracticeEasy
Passage / Data

Answer the following questions based on the information given below.

Schematic of walkways and lakes

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.

SegmentLength (m)SegmentLength (m)
AB, HG, IJ, PO150HI, GJ, FK, EL200
BC, CD300GF, FE300
JK, KL300ON, NM300
AH, IP, BG, JO400CF, KN, DE, LM400
GI (diagonal)250OK (diagonal)500

Coordinates (m), origin at P, taking the grid columns at x = 0, 150, 450, 750 and rows at y = 0, 400, 600, 1000: A(0,1000) B(150,1000) C(450,1000) D(750,1000); H(0,600) G(150,600) F(450,600) E(750,600); I(0,400) J(150,400) K(450,400) L(750,400); P(0,0) O(150,0) N(450,0) M(750,0). Lakes: C-D-E-F, G-F-K-J, K-L-M-N.

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?

Answer & solution

  • A

    3000

  • B

    2700

  • C

    3100

  • 3200

Solution

Easy

Model the walkways as a weighted graph and find the shortest distances between L, P (post office) and B (bank). The minimum round trip from L visiting both is L→P→B→L (or its reverse).

Distances (m): outer/inner segments — AB,HG,IJ,PO = 150; HI,GJ,FK,EL = 200; BC,CD,GF,FE,JK,KL,ON,NM = 300; AH,IP,BG,JO,CF,KN,DE,LM = 400; diagonals GI = 250, OK = 500. Post office at P, bank at B, residence at L.

Shortest pathRoute usedDistance (m)
L → PL-K-O-P (OK diagonal)950
P → BP-I-G-B1050
B → LB-G-F-E-L1200
1

Shortest L to P. The cheapest route uses the OK diagonal: L-K-O-P.

L→300K→500O→150P(OK = 500 diagonal)⇒ d(L,P)=300+500+150⇒ d(L,P)=950\begin{aligned} &L\xrightarrow{300}K\xrightarrow{500}O\xrightarrow{150}P \quad\text{(OK = 500 diagonal)}\\ &\Rightarrow\ d(L,P)=300+500+150\\ &\Rightarrow\ d(L,P)=950 \end{aligned}
2

Shortest P to B and B to L. From the chart graph.

P→400I→250G→400B⇒ d(P,B)=1050(GI diagonal)B→400G→300F→300E→200L⇒ d(B,L)=1200\begin{aligned} &P\xrightarrow{400}I\xrightarrow{250}G\xrightarrow{400}B \Rightarrow\ d(P,B)=1050 \quad\text{(GI diagonal)}\\ &B\xrightarrow{400}G\xrightarrow{300}F\xrightarrow{300}E\xrightarrow{200}L \Rightarrow\ d(B,L)=1200 \end{aligned}
3

Best round trip. Add the three legs (the reverse order gives the same total).

d(L,P)+d(P,B)+d(B,L)⇒ 950+1050+1200(steps 1–2)⇒ 3200\begin{aligned} &d(L,P)+d(P,B)+d(B,L)\\ &\Rightarrow\ 950+1050+1200 \quad\text{(steps 1–2)}\\ &\Rightarrow\ 3200 \end{aligned}
3200 m3200\ \text{m}
CAT 2024 Slot 2 DILR Q1: One resident whose house is located at L, needs to visit the post office as well as the bank. What is the mini — Solution | TheCATExam