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Year

CAT 2024

Section

Data

Topic

Network Flow Diagrams

Difficulty

Hard

Question

Slot-3

Read the passage and answer the questions below.

Passage:

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\mathrm{V} 1, \mathrm{~V} 2, and V 3 . 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.

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 RC\mathrm{R}-\mathrm{C} and V 3 is 12 km .

Question 1

Which of the following statements is correct?

There is no ATM placed at the (R-C, V2) intersection.

The ATM placed at the (R-C, V2) intersection has a cash requirement of Rs. 9 Lakhs.

The ATM placed at the (R-C, V2) intersection has a cash requirement of Rs. 8 Lakhs.

The cash requirement of the ATM placed at the (R-C, V2) intersection cannot be uniquely determined.

Question 2

How many ATMs have cash requirements of Rs. 10 Lakhs or more?

Question 3

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.

Only Statement A

Neither Statement A nor Statement B

Only Statement B

Both Statement A and Statement B

Question 4

What best can be said about the road distance (in km) between the ATMs having the second highest and the second lowest cash requirements?

4 km

7 km

5 km

Either 4 km or 7 km

Question 5

What is the number of ATMs whose locations and cash requirements can both be uniquely determined?

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