P, Q, R, S and T reside in a 5-storeyed (Ground + 4) building, and each of them resides on a separate floor. Further, 1. T does not reside on the topmost floor. 2. Q does not reside on the ground floor. 3. S resides on one storey above that of P and one storey below that of R. To know as to which of the 5 persons resides on the ground floor which of the above statements are sufficient/insufficient?
- A1 and 3 are sufficient
- B2 and 3 are sufficient
- C1, 2 and 3 are sufficient
- D1, 2 | 3 are insufficientCorrect
Explanation
The problem asks to identify who resides on the ground floor using the given statements. There are 5 floors (Ground, 1, 2, 3, 4) and 5 persons (P, Q, R, S, T).
Let's analyze the statements:
- T does not reside on the topmost floor (Floor 4).
- Q does not reside on the ground floor.
- S resides on one storey above P and one storey below R. This means R, S, P must reside on consecutive floors in that order (R-S-P block).
Now, let's combine all three statements and check the possibilities for the R-S-P block:
Possibility 1: R-S-P occupies floors 4, 3, 2. Floor 4: R Floor 3: S Floor 2: P Remaining persons: Q, T Remaining floors: 1, Ground Applying statement 1 (T not on Floor 4) is satisfied as T is not R. Applying statement 2 (Q not on Ground Floor): If Q cannot be on the ground floor, Q must be on Floor 1. This leaves T for the Ground Floor. In this case, T resides on the Ground Floor.
Possibility 2: R-S-P occupies floors 3, 2, 1. Floor 3: R Floor 2: S Floor 1: P Remaining persons: Q, T Remaining floors: 4, Ground Applying statement 1 (T not on Floor 4): T cannot be on Floor 4. So, T must be on the Ground Floor. Applying statement 2 (Q not on Ground Floor) is satisfied as T is on Ground. This leaves Q for Floor 4. In this case, T resides on the Ground Floor.
Possibility 3: R-S-P occupies floors 2, 1, Ground. Floor 2: R Floor 1: S Ground: P Remaining persons: Q, T Remaining floors: 4, 3 Applying statement 1 (T not on Floor 4): T cannot be on Floor 4. So, T must be on Floor 3. Applying statement 2 (Q not on Ground Floor) is satisfied as P is on the Ground Floor. This leaves Q for Floor 4. In this case, P resides on the Ground Floor.
Since combining all three statements leads to two different possibilities for the person on the ground floor (T in Possibility 1 and 2, or P in Possibility 3), the statements are insufficient to definitively determine who resides on the ground floor.
Therefore, statements 1, 2 and 3 are insufficient.
The final answer is D

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