CAT 2024 Slot 3 — DILR Question 14
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 / total (Rs. Lakhs) | V1 | V2 | V3 | Row total |
|---|---|---|---|---|
| R-A | · | · | · | 22 |
| R-B | · | · | · | 20 |
| R-C | · | · | · | 20 |
| Column total | 15 | 21 | 26 | 62 |
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.
What is the number of ATMs whose locations and cash requirements can both be uniquely determined?
Answer & solution
Answer: 3
Hard
List both valid full arrangements and keep only the ATMs whose location and cash are identical in both.
Arrangement I (V1=): (R-A,V1)=15, (R-A,V3)=7, (R-B,V2)=12, (R-B,V3)=8, (R-C,V2)=9, (R-C,V3)=11.
Arrangement II (V1=): (R-A,V1)=7, (R-A,V3)=15, (R-B,V1)=8, (R-B,V2)=12, (R-C,V2)=9, (R-C,V3)=11.
Compare the two arrangements cell by cell. The 7, 8 and 15 ATMs shift positions; three ATMs never move.