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CAT 2018 Slot 2 · DILR · Allocation and Selection · hard

CAT 2018 Slot 2 DILR: Warehouse Dispatch

A warehouse must dispatch six orders — O1 to O6 — using three trucks, T1, T2 and T3. Each truck carries exactly two orders, and every truck has a maximum carrying capacity of 300 kg. The weight of each order is given below.

| Order | O1 | O2 | O3 | O4 | O5 | O6 |
|---|---|---|---|---|---|---|
| Weight (kg) | 120 | 150 | 90 | 200 | 80 | 160 |

It is known that:
1. O1 and O2 are loaded onto the same truck.
2. O4 and O5 are loaded onto the same truck.
3. Truck T2 carries the heaviest combined load among the three trucks.
4. Truck T1's combined load is less than Truck T3's combined load.

Loading proceeds at a constant rate of 5 kg per minute per truck.

Question 1

Single correct option

Which truck carries order O4?
  1. A. T1
  2. B. T2
  3. C. T3
  4. D. Cannot be determined
Show answer and solution

Answer: (B) T2

Since O1,O2 must be together and O4,O5 must be together, the only weight-feasible (≤300kg) pairing of the remaining orders (O3=90, O6=160) keeps them together too: (O1,O2)=270kg, (O3,O6)=250kg, (O4,O5)=280kg — this is the only split consistent with clues 1 and 2 among all capacity-feasible pairings. T2 carries the heaviest load (280kg) = (O4,O5). So O4 is on T2.

Question 2

Numerical answer

What is the combined load (in kg) carried by truck T1?
Show answer and solution

Answer: 250

From the deduction above, the three loads are (O1,O2)=270kg, (O3,O6)=250kg, (O4,O5)=280kg. T2=280kg (heaviest). Since T1's load < T3's load, and the remaining two loads are 270 and 250, T1=250kg (O3,O6) and T3=270kg (O1,O2).

Question 3

Single correct option

If T2 starts loading at 9:15 AM, and loading proceeds at 5 kg per minute, at what time does T2 finish loading?
  1. A. 10:01 AM
  2. B. 10:05 AM
  3. C. 10:11 AM
  4. D. 10:15 AM
Show answer and solution

Answer: (C) 10:11 AM

T2's load is 280 kg. Loading time = 280/5 = 56 minutes. 9:15 AM + 56 minutes = 10:11 AM.

Question 4

Numerical answer

What is the difference (in kg) between the heaviest and the lightest truck loads?
Show answer and solution

Answer: 30

Loads are T1=250kg, T2=280kg, T3=270kg. Heaviest − lightest = 280 − 250 = 30 kg.
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Original question written in the CAT 2018 Slot 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake