CAT 2025 Slot 1 · DILR · Question 11
CAT 2025 Slot 1 previous year question on Arrangement Based Puzzes, with the answer and a step-by-step solution.
Set 3: Seven Chairs Around a Round Table — this question belongs to a set. Read the full set with all 4 questions →
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.
The four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6.
Davies occupies Chair 2 after Turn 1 and Chair 4 after Turn 5, and Chhavi occupies Chair 7 after Turn 2.
Answer & solution
Answer: 4
Davies first moves in Turn 4, so his position after Turn 1 is where he started — Chair 2.
Chhavi first moves in Turn 3, so her position after Turn 2 is also her starting chair — Chair 7.
Aslam starts next to Chhavi, so he began on Chair 1 or Chair 6.
Davies must have empty chairs on both sides, which means Chairs 1 and 3 were empty.
That rules out Chair 1 for Aslam, so Aslam began on Chair 6.
Bashir also needs empty chairs on both sides, and the occupied chairs so far are 2, 6 and 7.
Chair 3 fails because Chair 2 is taken, and Chair 5 fails because Chair 6 is taken.
Chair 4 works, with Chairs 3 and 5 both empty.
So Bashir started on Chair 4.
Shortcut. The two "isolated" friends do the work: Davies at Chair 2 immediately empties Chairs 1 and 3, which pins Aslam to Chair 6 and leaves Chair 4 as the only isolated seat remaining.
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