CAT 2025Slot 1DILRQuestion & SolutionQues & Sol
Data Set
A round table has seven chairs around it. The chairs are numbered 1 through 7 in a clockwise direction. Four friends, Aslam, Bashir, Chhavi, and Davies, sit on four of the chairs. In the starting position, Aslam and Chhavi are sitting next to each other, while for Bashir as well as Davies, there are empty chairs on either side of the chairs that are sitting on.
The friends take turns moving either clockwise or counterclockwise from their chair. The friend who has to move in a turn occupies the first empty chair in whichever direction (s)he chooses to move. Aslam moves first (Turn 1), followed by Bashir, Chhavi, and Davies (Turns 2, 3, and 4, respectively). Then Aslam moves again followed by Bashir, and Chhavi (Turns 5, 6, and 7, respectively).
The following information is known
1. The four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6.
2. Davies occupies Chair 2 after Turn 1 and Chair 4 after Turn 5, and Chhavi occupies Chair 7 after Turn 2.
Question 1
What is the number of the chair initially occupied by Bashir?
Solution
1. Setup
There are 7 chairs numbered clockwise from 1 to 7.
The four friends are Aslam (A), Bashir (B), Chhavi (C), and Davies (D).
The turn order is:
| Turn | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Mover | A | B | C | D | A | B | C |
Initially:
- Asha and Chhavi are sitting next to each other.
- Both chairs adjacent to Bashir are empty.
- Both chairs adjacent to Davies are empty.
We are also given:
- Davies is at Chair 2 after Turn 1.
- Chhavi is at Chair 7 after Turn 2.
- Davies is at Chair 4 after Turn 5.
- All four friends occupy adjacent chairs only after Turns 2 and 6.
2. Solution
Since Davies is at Chair 2 after Turn 1, and both chairs adjacent to Davies were initially empty, Chairs 1 and 3 must initially be empty.
Therefore, Aslam and Chhavi must occupy Chairs 6 and 7.
Since Aslam and Chhavi are adjacent, and Chair 2 is occupied by Davies, the remaining friend, Bashir, must initially occupy Chair 4.
Thus, the initial arrangement is:
| Chair | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Person | Empty | Davies | Empty | Bashir | Empty | Aslam | Chhavi |
The subsequent movements are consistent with the conditions that all four friends occupy adjacent chairs after Turns 2 and 6.
Therefore, Bashir initially occupied Chair 4.
3. Final Answer
Answer = 4 ✅
Bashir initially occupied Chair 4.
Question 2
Who sits on the chair numbered 4 at the end of Turn 3?
Solution
1. Setup
Using the valid sequence of movements, the positions after Turn 3 are:
- Aslam = Chair 1
- Bashir = Chair 3
- Chhavi = Chair 6
- Davies = Chair 2
2. Solution
Davies moves to Chair 4 only on Turn 4.
Therefore, at the end of Turn 3, Chair 4 is empty.
3. Final Answer
Answer = Option D ✅
No one sits on Chair 4 at the end of Turn 3.
Question 3
Which of the chairs are occupied at the end of Turn 6?
Solution
1. Setup
At the end of Turn 6, the positions of the four friends are:
| Friend | Chair |
|---|---|
| Aslam | 7 |
| Bashir | 5 |
| Chhavi | 6 |
| Davies | 4 |
2. Solution
Therefore, the occupied chairs are:
$$ {4,5,6,7} $$
These four chairs form a contiguous block, which is consistent with the condition that all four friends occupy adjacent chairs at the end of Turn 6.
3. Final Answer
Answer = Option A ✅
Chairs numbered 4, 5, 6, and 7 are occupied at the end of Turn 6.
Question 4
Which of the following BEST describes the friends sitting on chairs adjacent to the one occupied by Bashir at the end of Turn 7?
Solution
1. Setup
At the end of Turn 6:
| Friend | Chair |
|---|---|
| Aslam | 7 |
| Bashir | 5 |
| Chhavi | 6 |
| Davies | 4 |
In Turn 7, Chhavi moves from Chair 6 to the first empty chair in her chosen direction. The possible final positions for Chhavi are Chair 1 or Chair 3.
Therefore, Bashir remains at Chair 5, while Chair 4 is occupied by Davies and Chair 6 is empty.
2. Solution
The chairs adjacent to Bashir at Chair 5 are:
$$ 4 \text{ and } 6 $$
- Chair 4 → Davies
- Chair 6 → Empty
Hence, only Davies is sitting adjacent to Bashir.
3. Final Answer
Answer = Option B ✅
Davies only sits on a chair adjacent to Bashir at the end of Turn 7.