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CAT 2024 Slot 3 — DILR Question 12

Mixed PracticeEasy
Passage / Data

Answer the following questions based on the information given below.

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.

Road network grid of R-A/R-B/R-C and V1/V2/V3 with totals and inter-intersection distances

Road / total (Rs. Lakhs)V1V2V3Row total
R-A···22
R-B···20
R-C···20
Column total15212662

Distances between adjacent intersections (in km): along R-A, V1–V2 = 4 km and V2–V3 = 7 km; along V3, R-A–R-B = 3 km and R-B–R-C = 5 km.

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.

Which of the following two statements is/are DEFINITELY true?

Statement A: Each of R-A, R-B, and R-C has two ATMs.
Statement B: Each of V1, V2, and V3 has two ATMs.

Answer & solution

  • Only Statement A

  • B

    Both Statement A and Statement B

  • C

    Neither Statement A nor Statement B

  • D

    Only Statement B

Solution

Hard

With two ATMs per row (6 over 3 rows), Statement A is forced. For columns, the V1=15 total admits two arrangements — one gives 2-2-2 columns, the other 1-2-3 — so Statement B is only sometimes true.

R-A={7,15}\{7,15\}, R-B={8,12}\{8,12\} with 1212 at V2, R-C={9,11}\{9,11\} with 99 at V2. Remaining cells to fill: V1 (=15) and V3 (=26) from values {7,15}\{7,15\} (R-A), 88 (R-B), 1111 (R-C).

1

Statement A is definitely true. Six ATMs over three rows with row totals achievable only by pairs means each road has exactly two ATMs.

R-A={7,15}, R-B={8,12}, R-C={9,11}⇒ each road has exactly 2 ATMs\begin{aligned} &\text{R-A}=\{7,15\},\ \text{R-B}=\{8,12\},\ \text{R-C}=\{9,11\}\\ &\Rightarrow\ \text{each road has exactly }2\ \text{ATMs} \end{aligned}
2

Statement B is not definite. Column V1 =15=15 can be made as {15}\{15\} or {7,8}\{7,8\}, giving different column counts.

V1={15} ⇒ columns 1-2-3 (not two each)⇒ V1={7,8} ⇒ columns 2-2-2 (two each)⇒ Statement B only sometimes holds\begin{aligned} &\text{V1}=\{15\}\ \Rightarrow\ \text{columns }1\text{-}2\text{-}3\ (\text{not two each})\\ &\Rightarrow\ \text{V1}=\{7,8\}\ \Rightarrow\ \text{columns }2\text{-}2\text{-}2\ (\text{two each})\\ &\Rightarrow\ \text{Statement B only sometimes holds} \end{aligned}

Only Statement A

CAT 2024 Slot 3 DILR Q12: Which of the following two statements is/are DEFINITELY true? Statement A: Each of R-A, R-B, and R-C has two A — Solution | TheCATExam