CAT 2024 Slot 3 DILR Set 5 Q18–Q22

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2024 Slot 3, with 5 questions (Routes & Networks). Answers are CAT's official key.

The set

This set relies on a figure in the original paper, which is not reproduced here. The questions and answers are 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.

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.

[Figure in the original paper]

Question 18

Which of the following statements is correct?
  1. A
    The ATM placed at the (R-C, V2) intersection has a cash requirement of Rs. 9 Lakhs.
  2. B
    There is no ATM placed at the (R-C, V2) intersection.
  3. C
    The ATM placed at the (R-C, V2) intersection has a cash requirement of Rs. 8 Lakhs.
  4. D
    The cash requirement of the ATM placed at the (R-C, V2) intersection cannot be uniquely determined.

Answer: (A) The ATM placed at the (R-C, V2) intersection has a cash requirement of Rs. 9 Lakhs. Routes & Networks MCQ

Solution

  1. Six distinct values from 7 to 15 including 7 and 15, total \(22 + 20 + 20 = 62\); the other four sum to 40 from 8-14: \(\{8,9,10,13\}\) or \(\{8,9,11,12\}\).
  2. 7 and 15 share a road; only R-A (22) fits, so R-A holds exactly 7 and 15. R-B and R-C each sum to 20, possible only with \(\{8,12\}\) and \(\{9,11\}\).
  3. Columns 15, 21, 26: either 15 at V1 alone (then V3 = 7 + 8 + 11, V2 = 12 + 9) or 7 and 8 at V1 (then V2 = 12 + 9, V3 = 15 + 11).
  4. Fact 2: 12 is 12 km from an ATM at (R-C, V3). Both cases force 12 at (R-B, V2) and R-C = 9 at V2, 11 at V3 (distance \(7 + 5 = 12\)). Case 1: R-A 15@V1, 7@V3, 8@(R-B,V3). Case 2: R-A 7@V1, 15@V3, 8@(R-B,V1).
  5. In both cases (R-C, V2) holds 9.

Question 19

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

TITA: type in the answer. There are no options and no negative marking.

Answer: 3 Routes & Networks TITA

Solution

  1. Six distinct values from 7 to 15 including 7 and 15, total \(22 + 20 + 20 = 62\); the other four sum to 40 from 8-14: \(\{8,9,10,13\}\) or \(\{8,9,11,12\}\).
  2. 7 and 15 share a road; only R-A (22) fits, so R-A holds exactly 7 and 15. R-B and R-C each sum to 20, possible only with \(\{8,12\}\) and \(\{9,11\}\).
  3. Columns 15, 21, 26: either 15 at V1 alone (then V3 = 7 + 8 + 11, V2 = 12 + 9) or 7 and 8 at V1 (then V2 = 12 + 9, V3 = 15 + 11).
  4. Fact 2: 12 is 12 km from an ATM at (R-C, V3). Both cases force 12 at (R-B, V2) and R-C = 9 at V2, 11 at V3 (distance \(7 + 5 = 12\)). Case 1: R-A 15@V1, 7@V3, 8@(R-B,V3). Case 2: R-A 7@V1, 15@V3, 8@(R-B,V1).
  5. Values 10 or more: 11, 12, 15. Answer: 3.

Question 20

Which of the following two statements is/are DEFINITELY true?
A)Statement A: Each of R-A, R-B, and R-C has two ATMs.
B)Statement B: Each of V1, V2, and V3 has two ATMs.
  1. A
    Both Statement A and Statement B
  2. B
    Neither Statement A nor Statement B
  3. C
    Only Statement A
  4. D
    Only Statement B

Answer: (C) Only Statement A Routes & Networks MCQ

Solution

  1. Six distinct values from 7 to 15 including 7 and 15, total \(22 + 20 + 20 = 62\); the other four sum to 40 from 8-14: \(\{8,9,10,13\}\) or \(\{8,9,11,12\}\).
  2. 7 and 15 share a road; only R-A (22) fits, so R-A holds exactly 7 and 15. R-B and R-C each sum to 20, possible only with \(\{8,12\}\) and \(\{9,11\}\).
  3. Columns 15, 21, 26: either 15 at V1 alone (then V3 = 7 + 8 + 11, V2 = 12 + 9) or 7 and 8 at V1 (then V2 = 12 + 9, V3 = 15 + 11).
  4. Fact 2: 12 is 12 km from an ATM at (R-C, V3). Both cases force 12 at (R-B, V2) and R-C = 9 at V2, 11 at V3 (distance \(7 + 5 = 12\)). Case 1: R-A 15@V1, 7@V3, 8@(R-B,V3). Case 2: R-A 7@V1, 15@V3, 8@(R-B,V1).
  5. Every row has two ATMs in both cases (A true). Case 1 has V1 with only one ATM and V3 with three, so B is not definite. Only A.

Question 21

What best can be said about the road distance (in km) between the ATMs having the second highest and the second lowest cash requirements?
  1. A
    7 km
  2. B
    5 km
  3. C
    4 km
  4. D
    Either 4 km or 7 km

Answer: (D) Either 4 km or 7 km Routes & Networks MCQ

Solution

  1. Six distinct values from 7 to 15 including 7 and 15, total \(22 + 20 + 20 = 62\); the other four sum to 40 from 8-14: \(\{8,9,10,13\}\) or \(\{8,9,11,12\}\).
  2. 7 and 15 share a road; only R-A (22) fits, so R-A holds exactly 7 and 15. R-B and R-C each sum to 20, possible only with \(\{8,12\}\) and \(\{9,11\}\).
  3. Columns 15, 21, 26: either 15 at V1 alone (then V3 = 7 + 8 + 11, V2 = 12 + 9) or 7 and 8 at V1 (then V2 = 12 + 9, V3 = 15 + 11).
  4. Fact 2: 12 is 12 km from an ATM at (R-C, V3). Both cases force 12 at (R-B, V2) and R-C = 9 at V2, 11 at V3 (distance \(7 + 5 = 12\)). Case 1: R-A 15@V1, 7@V3, 8@(R-B,V3). Case 2: R-A 7@V1, 15@V3, 8@(R-B,V1).
  5. 12 at (R-B, V2); 8 at (R-B, V3) gives 7 km, at (R-B, V1) gives 4 km. Either 4 or 7.

Question 22

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

TITA: type in the answer. There are no options and no negative marking.

Answer: 3 Routes & Networks TITA

Solution

  1. Six distinct values from 7 to 15 including 7 and 15, total \(22 + 20 + 20 = 62\); the other four sum to 40 from 8-14: \(\{8,9,10,13\}\) or \(\{8,9,11,12\}\).
  2. 7 and 15 share a road; only R-A (22) fits, so R-A holds exactly 7 and 15. R-B and R-C each sum to 20, possible only with \(\{8,12\}\) and \(\{9,11\}\).
  3. Columns 15, 21, 26: either 15 at V1 alone (then V3 = 7 + 8 + 11, V2 = 12 + 9) or 7 and 8 at V1 (then V2 = 12 + 9, V3 = 15 + 11).
  4. Fact 2: 12 is 12 km from an ATM at (R-C, V3). Both cases force 12 at (R-B, V2) and R-C = 9 at V2, 11 at V3 (distance \(7 + 5 = 12\)). Case 1: R-A 15@V1, 7@V3, 8@(R-B,V3). Case 2: R-A 7@V1, 15@V3, 8@(R-B,V1).
  5. Fixed in both cases: 12 at (R-B, V2), 9 at (R-C, V2), 11 at (R-C, V3). 7, 15 and 8 move. Answer: 3.

Same concept in other years

See every question on Values placed in a grid layout, deduced from row and column totals.

More Routes & Networks questions from CAT

All 41 Routes & Networks questions asked since 2017.