Analytical Reasoning Question No. 80
📋 Scenario: Six duty workers—Ali, Bilal, Ghulam, Jamal, Muneer, and Tanveer—are planning to perform a duty program consisting entirely of three shifts. Each shift requires two fire men, one gas expert, and a driver. Each worker must perform duty in at least one shift, and each worker can perform duty of, at most, one role in a shift. No worker can perform duty of the same type of role (fire man, gas expert, or driver) in two successive shifts.
Constraints:
1. Ali can perform duty of fire man only, and must perform duty in the first shift.
2. Bilal can perform duty of fire man or driver.
3. Ghulam can perform duty of fire man or gas expert.
4. Jamal can perform duty of gas expert only.
5. Muneer can perform duty of fire man or driver.
6. Tanveer can perform duty of driver only.
Constraints:
1. Ali can perform duty of fire man only, and must perform duty in the first shift.
2. Bilal can perform duty of fire man or driver.
3. Ghulam can perform duty of fire man or gas expert.
4. Jamal can perform duty of gas expert only.
5. Muneer can perform duty of fire man or driver.
6. Tanveer can perform duty of driver only.
1️⃣ Any of the following duty workers could perform duty in the second shift EXCEPT
2️⃣ If Ghulam can perform duty of gas expert in the first shift, which of the following must be true?
3️⃣ If Ali, Bilal, Ghulam, and Jamal perform duty in the first shift, which of the following could be the group of duty workers playing in the second shift?
4️⃣ Which of the following groups of duty workers includes all those, and only those, who CANNOT be scheduled to perform duty in all three shifts, no matter what schedule is devised?
| Worker | Allowed Roles | Restriction / Notes |
|---|---|---|
| Ali | Fire man only | Must be in shift 1; same role in successive shifts prohibited → cannot work all 3 shifts if same role? Actually Fire man only, but cannot be fire man in two successive shifts → max 2 shifts possible (shift1 & shift3 only possible). So impossible in all 3 shifts. |
| Bilal | Fire man, Driver | Can alternate roles potentially, but has flexibility → possible for 3 shifts. |
| Ghulam | Fire man, Gas expert | Flexible → possible 3 shifts by switching roles. |
| Jamal | Gas expert only | Single role only → cannot serve gas expert in successive shifts, so at most shift1 & shift3, not all 3 shifts. |
| Muneer | Fire man, Driver | Two roles → can alternate → possible for 3 shifts. |
| Tanveer | Driver only | Only driver, cannot be driver in consecutive shifts → max 2 shifts, never all three. |
✅ Explanation: Ali (only fire man), Jamal (only gas expert), Tanveer (only driver) each have only one role type, so they cannot be scheduled in three shifts due to "no same role in successive shifts" rule. Hence group B (Ali, Jamal, Tanveer) is exactly the set that CANNOT be in all three shifts.
5️⃣ Unavailability of which of the following duty workers would still permit scheduling the five remaining players so that the proposed program could be performed?
| If removed | Remaining five feasibility? | Reason |
|---|---|---|
| Bilal | Possible ✅ | Ali (fire), Ghulam (fire/gas), Jamal (gas), Muneer (fire/driver), Tanveer (driver). Can manage 2 firemen, 1 gas, 1 driver each shift with role alternation. |
| Ghulam | Possible ✅ | Ali (fire), Bilal (fire/driver), Jamal (gas), Muneer (fire/driver), Tanveer (driver). Enough flexibility to cover shifts. |
| Jamal | Impossible ❌ | Without Jamal, only gas expert possible? Ghulam can be gas expert, but we need gas expert each shift (3 shifts). Only Ghulam can serve as gas expert (Ali no, Bilal no, Muneer no, Tanveer no). Ghulam cannot be gas expert in two successive shifts → can't cover all three shifts alone, so program fails. |
| Muneer | Possible ✅ | Ali (fire), Bilal (fire/driver), Ghulam (fire/gas), Jamal (gas), Tanveer (driver). Can fill all roles across 3 shifts with rotation. |
| Tanveer | Possible ✅ | Ali, Bilal, Ghulam, Jamal, Muneer — driver roles can be taken by Bilal or Muneer. With flexible roles, feasible. |
📌 Inference: Only removal of Jamal creates impossibility because only Ghulam remains as gas expert and cannot serve consecutive shifts as gas expert. Hence answer: Jamal.
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