CAT — Circular Arrangement
8 questions, free to view. Click any question to see the answer and explanation.
Seven children, Aarav, Bina, Chirag, Diya, Eshan, Farhan, and Gaurav, are sitting in a circle facing inside (not necessarily in the same order) and playing a game of 'Passing the Buck'.
The game is played over 10 rounds. In each round, the child holding the Buck must pass it directly to a child sitting in one of the following positions:
• Immediately to the left;
• Immediate to the right;
• Second to the left; or
• Second to the right.
The game starts with Bina passing the Buck and ends with Chirag receiving the Buck. The table below provides some information about the pass types and the child receiving the Buck. Some information is missing and labelled as '?'.
Who is sitting immediately to the right of Bina?
Eshan
Aarav
Farhan
Chirag
Eshan
In Round 8, Diya receives the Buck. In Round 9, she passes it in such a way that Farhan receives it.
If Farhan sits to the immediate left of Diya, then there is no way Farhan passes it in a way receives it.
Therefore, Diya must pass second to the right and then Farhan must pass immediate to the right and Chirag received it.
Final arrangement looks like:
Eshan is sitting immediately to the right of Bina.
Who is sitting third to the left of Eshan?
Chirag
Aarav
Divya
Gaurav
Chirag
In Round 8, Diya receives the Buck. In Round 9, she passes it in such a way that Farhan receives it.
If Farhan sits to the immediate left of Diya, then there is no way Farhan passes it in a way receives it.
Therefore, Diya must pass second to the right and then Farhan must pass immediate to the right and Chirag received it.
Final arrangement looks like:
Chirag is sitting third to the left of Eshan.
For which of the following pass types can the total number of occurrences be uniquely determined?
Immediately to the left
Second to the right
Immediately to the right
Second to the left
Immediately to the right
In Round 8, Diya receives the Buck. In Round 9, she passes it in such a way that Farhan receives it.
If Farhan sits to the immediate left of Diya, then there is no way Farhan passes it in a way receives it.
Therefore, Diya must pass second to the right and then Farhan must pass immediate to the right and Chirag received it.
Final arrangement looks like:
For Immediately to the right pass type the total number of occurrences can be uniquely determined.
For which of the following children is it possible to determine how many times they received the Buck?
Eshan
Gaurav
Bina
Farhan
Gaurav
In Round 8, Diya receives the Buck. In Round 9, she passes it in such a way that Farhan receives it.
If Farhan sits to the immediate left of Diya, then there is no way Farhan passes it in a way receives it.
Therefore, Diya must pass second to the right and then Farhan must pass immediate to the right and Chirag received it.
Final arrangement looks like:
For Gaurav it is possible to determine the number of times he received the Buck due to round 4.
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.
What is the number of the chair initially occupied by Bashir?
Step 1:
Initially, Aslam and Chhavi are seated next to each other, whereas Bashir and Davies each have an empty chair on both sides. Since the seating arrangement is circular, the relative placement of Aslam and Chhavi can be fixed arbitrarily without affecting the solution.
From Condition (1), the four friends occupy four consecutive chairs only after Turns 2 and 6. If Aslam were to move counterclockwise, they would fail to occupy adjacent chairs at the end of Turn 2. Hence, Aslam must move clockwise in Turn 1, which means Bashir moves counterclockwise.
Using Condition (2), Davies is on Chair 2 after Turn 1, while Chhavi reaches Chair 7 after Turn 2.
The arrangements after Turns 1 and 2 are shown below.
Step 2:
During Turn 3, Chhavi moves counterclockwise and occupies Chair 6.
From Condition (2), Davies must be on Chair 4 after Turn 5. Therefore, in Turn 4, Davies moves clockwise to Chair 4.
In Turn 5, Aslam moves counterclockwise and occupies Chair 7.
Again applying Condition (1), the four friends sit on adjacent chairs only at the end of Turns 2 and 6. Hence, in Turn 6, Bashir moves clockwise and occupies Chair 5.
Finally, in Turn 7, Chhavi can move either clockwise or counterclockwise, ending up on Chair 1 or Chair 3, respectively.
Therefore, Bashir initially occupied Chair 4.
Who sits on the chair numbered 4 at the end of Turn 3?
Bashir
Chhavi
Davies
No one
No one
Step 1:
Initially, Aslam and Chhavi are seated next to each other, whereas Bashir and Davies each have an empty chair on both sides. Since the seating arrangement is circular, the relative placement of Aslam and Chhavi can be fixed arbitrarily without affecting the solution.
From Condition (1), the four friends occupy four consecutive chairs only after Turns 2 and 6. If Aslam were to move counterclockwise, they would fail to occupy adjacent chairs at the end of Turn 2. Hence, Aslam must move clockwise in Turn 1, which means Bashir moves counterclockwise.
Using Condition (2), Davies is on Chair 2 after Turn 1, while Chhavi reaches Chair 7 after Turn 2.
The arrangements after Turns 1 and 2 are shown below.
Step 2:
During Turn 3, Chhavi moves counterclockwise and occupies Chair 6.
From Condition (2), Davies must be on Chair 4 after Turn 5. Therefore, in Turn 4, Davies moves clockwise to Chair 4.
In Turn 5, Aslam moves counterclockwise and occupies Chair 7.
Again applying Condition (1), the four friends sit on adjacent chairs only at the end of Turns 2 and 6. Hence, in Turn 6, Bashir moves clockwise and occupies Chair 5.
Finally, in Turn 7, Chhavi can move either clockwise or counterclockwise, ending up on Chair 1 or Chair 3, respectively.
No one sits on the chair numbered 4 at the end of Turn 3.
Which of the chairs are occupied at the end of Turn 6?
Chairs numbered 4, 5, 6, and 7
Chairs numbered 2, 3, 4, and 5
Chairs numbered 1, 2, 3, and 4
Chairs numbered 1, 2, 6, and 7
Chairs numbered 4, 5, 6, and 7
Step 1:
Initially, Aslam and Chhavi are seated next to each other, whereas Bashir and Davies each have an empty chair on both sides. Since the seating arrangement is circular, the relative placement of Aslam and Chhavi can be fixed arbitrarily without affecting the solution.
From Condition (1), the four friends occupy four consecutive chairs only after Turns 2 and 6. If Aslam were to move counterclockwise, they would fail to occupy adjacent chairs at the end of Turn 2. Hence, Aslam must move clockwise in Turn 1, which means Bashir moves counterclockwise.
Using Condition (2), Davies is on Chair 2 after Turn 1, while Chhavi reaches Chair 7 after Turn 2.
The arrangements after Turns 1 and 2 are shown below.
Step 2:
During Turn 3, Chhavi moves counterclockwise and occupies Chair 6.
From Condition (2), Davies must be on Chair 4 after Turn 5. Therefore, in Turn 4, Davies moves clockwise to Chair 4.
In Turn 5, Aslam moves counterclockwise and occupies Chair 7.
Again applying Condition (1), the four friends sit on adjacent chairs only at the end of Turns 2 and 6. Hence, in Turn 6, Bashir moves clockwise and occupies Chair 5.
Finally, in Turn 7, Chhavi can move either clockwise or counterclockwise, ending up on Chair 1 or Chair 3, respectively.
Chairs numbered 4, 5, 6, and 7 are occupied at the end of Turn 6.
Which of the following BEST describes the friends sitting on chairs adjacent to the one occupied by Bashir at the end of Turn 7?
Aslam and Chhavi
Chhavi only
Davies only
Chhavi and Davies
Davies only
Step 1:
Initially, Aslam and Chhavi are seated next to each other, whereas Bashir and Davies each have an empty chair on both sides. Since the seating arrangement is circular, the relative placement of Aslam and Chhavi can be fixed arbitrarily without affecting the solution.
From Condition (1), the four friends occupy four consecutive chairs only after Turns 2 and 6. If Aslam were to move counterclockwise, they would fail to occupy adjacent chairs at the end of Turn 2. Hence, Aslam must move clockwise in Turn 1, which means Bashir moves counterclockwise.
Using Condition (2), Davies is on Chair 2 after Turn 1, while Chhavi reaches Chair 7 after Turn 2.
The arrangements after Turns 1 and 2 are shown below.
Step 2:
During Turn 3, Chhavi moves counterclockwise and occupies Chair 6.
From Condition (2), Davies must be on Chair 4 after Turn 5. Therefore, in Turn 4, Davies moves clockwise to Chair 4.
In Turn 5, Aslam moves counterclockwise and occupies Chair 7.
Again applying Condition (1), the four friends sit on adjacent chairs only at the end of Turns 2 and 6. Hence, in Turn 6, Bashir moves clockwise and occupies Chair 5.
Finally, in Turn 7, Chhavi can move either clockwise or counterclockwise, ending up on Chair 1 or Chair 3, respectively.
At the end of Turn 7, only Davies is sitting on a chair adjacent to the one occupied by Bashir.
Want this as a timed attempt?
Log in free to attempt this topic with a real timer, analytics, streaks and bookmarks.