CAT — Arrangements
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The schematic diagram below shows 12 rectangular houses in a housing complex. House numbers are mentioned in the rectangles representing the houses. The houses are located in six columns – Column-A through Column-F, and two rows – Row-1 and Row-2. The houses are divided into two blocks - Block XX and Block YY. The diagram also shows two roads, one passing in front of the houses in Row-2 and another between the two blocks.
Some of the houses are occupied. The remaining ones are vacant and are the only ones available for sale.
The road adjacency value of a house is the number of its sides adjacent to a road. For example, the road adjacency values of C2, F2, and B1 are 2, 1, and 0, respectively. The neighbour count of a house is the number of sides of that house adjacent to occupied houses in the same block. For example, E1 and C1 can have the maximum possible neighbour counts of 3 and 2, respectively.
The base price of a vacant house is Rs. 10 lakhs if the house does not have a parking space, and Rs. 12 lakhs if it does. The quoted price (in lakhs of Rs.) of a vacant house is calculated as (base price) + 5 × (road adjacency value) + 3 × (neighbour count).
The following information is also known.
1. The maximum quoted price of a house in Block XX is Rs. 24 lakhs. The minimum quoted price of a house in block YY is Rs. 15 lakhs, and one such house is in Column-E.
2. Row-1 has two occupied houses, one in each block.
3. Both houses in Column-E are vacant. Each of Column-D and Column-F has at least one occupied house.
4. There is only one house with parking space in Block YY.
How many houses are vacant in Block XX?
Step 1:
The quoted price (in lakhs of rupees) is calculated as:
Quoted Price = Base Price + 5 × (Number of adjacent roads) + 3 × (Number of neighbouring occupied houses)
Thus,
QP = 10/12 + 5(0, 1, 2) + 3(0, 1, 2, 3)
Using conditions (1) and (2),
- 24 = 10 + 5 × 1 + 3 × 3
- 15 = 10 + 5 × 1 + 3 × 0 or 15 = 12 + 5 × 0 + 3 × 1
In Block XX, the highest quoted price is Rs. 24 lakh.
Hence, B1, A2, and C2 are occupied, while A1, B2, and C1 are vacant (i.e., available for sale).
Step 2:
From condition (3), E1 and E2 are vacant.
Also, from conditions (2) and (3), exactly one of D1 and F1 is occupied.
For E1,
Quoted Price = 15
= 12 + 5 × 0 + 3 × 1
Therefore, by condition (4), E1 is the only house in Block YY with a parking space.
Further, from condition (3), each of Column D and Column F contains at least one occupied house.
This gives two possibilities:
- If D1 is occupied, then F2 must also be occupied, while D2 may be either occupied or vacant.
- If F1 is occupied, then D2 must be occupied, while F2 may be either occupied or vacant.
Three houses A1, C1 and B2 are vacant in Block XX.
Which of the following houses is definitely occupied?
B1
A1
D2
F2
B1
Step 1:
The quoted price (in lakhs of rupees) is calculated as:
Quoted Price = Base Price + 5 × (Number of adjacent roads) + 3 × (Number of neighbouring occupied houses)
Thus,
QP = 10/12 + 5(0, 1, 2) + 3(0, 1, 2, 3)
Using conditions (1) and (2),
- 24 = 10 + 5 × 1 + 3 × 3
- 15 = 10 + 5 × 1 + 3 × 0 or 15 = 12 + 5 × 0 + 3 × 1
In Block XX, the highest quoted price is Rs. 24 lakh.
Hence, B1, A2, and C2 are occupied, while A1, B2, and C1 are vacant (i.e., available for sale).
Step 2:
From condition (3), E1 and E2 are vacant.
Also, from conditions (2) and (3), exactly one of D1 and F1 is occupied.
For E1,
Quoted Price = 15
= 12 + 5 × 0 + 3 × 1
Therefore, by condition (4), E1 is the only house in Block YY with a parking space.
Further, from condition (3), each of Column D and Column F contains at least one occupied house.
This gives two possibilities:
- If D1 is occupied, then F2 must also be occupied, while D2 may be either occupied or vacant.
- If F1 is occupied, then D2 must be occupied, while F2 may be either occupied or vacant.
House B1 is definitely occupied.
Which of the following options best describes the number of vacant houses in Row-2?
Exactly 3
Either 2 or 3
Either 3 or 4
Exactly 2
Either 2 or 3
Step 1:
The quoted price (in lakhs of rupees) is calculated as:
Quoted Price = Base Price + 5 × (Number of adjacent roads) + 3 × (Number of neighbouring occupied houses)
Thus,
QP = 10/12 + 5(0, 1, 2) + 3(0, 1, 2, 3)
Using conditions (1) and (2),
- 24 = 10 + 5 × 1 + 3 × 3
- 15 = 10 + 5 × 1 + 3 × 0 or 15 = 12 + 5 × 0 + 3 × 1
In Block XX, the highest quoted price is Rs. 24 lakh.
Hence, B1, A2, and C2 are occupied, while A1, B2, and C1 are vacant (i.e., available for sale).
Step 2:
From condition (3), E1 and E2 are vacant.
Also, from conditions (2) and (3), exactly one of D1 and F1 is occupied.
For E1,
Quoted Price = 15
= 12 + 5 × 0 + 3 × 1
Therefore, by condition (4), E1 is the only house in Block YY with a parking space.
Further, from condition (3), each of Column D and Column F contains at least one occupied house.
This gives two possibilities:
- If D1 is occupied, then F2 must also be occupied, while D2 may be either occupied or vacant.
- If F1 is occupied, then D2 must be occupied, while F2 may be either occupied or vacant.
The number of vacant houses in Row-2 is either 2 or 3.
What is the maximum possible quoted price (in lakhs of Rs.) for a vacant house in Column-E?
Step 1:
The quoted price (in lakhs of rupees) is calculated as:
Quoted Price = Base Price + 5 × (Number of adjacent roads) + 3 × (Number of neighbouring occupied houses)
Thus,
QP = 10/12 + 5(0, 1, 2) + 3(0, 1, 2, 3)
Using conditions (1) and (2),
- 24 = 10 + 5 × 1 + 3 × 3
- 15 = 10 + 5 × 1 + 3 × 0 or 15 = 12 + 5 × 0 + 3 × 1
In Block XX, the highest quoted price is Rs. 24 lakh.
Hence, B1, A2, and C2 are occupied, while A1, B2, and C1 are vacant (i.e., available for sale).
Step 2:
From condition (3), E1 and E2 are vacant.
Also, from conditions (2) and (3), exactly one of D1 and F1 is occupied.
For E1,
Quoted Price = 15
= 12 + 5 × 0 + 3 × 1
Therefore, by condition (4), E1 is the only house in Block YY with a parking space.
Further, from condition (3), each of Column D and Column F contains at least one occupied house.
This gives two possibilities:
- If D1 is occupied, then F2 must also be occupied, while D2 may be either occupied or vacant.
- If F1 is occupied, then D2 must be occupied, while F2 may be either occupied or vacant.
The maximum possible quoted price for a vacant house i.e., E2 in Column-E = 10 + 5 × 1 + 3 × 2 = Rs.21 lakhs.
Which house in Block YY has parking space?
E1
F1
F2
E2
E1
Step 1:
The quoted price (in lakhs of rupees) is calculated as:
Quoted Price = Base Price + 5 × (Number of adjacent roads) + 3 × (Number of neighbouring occupied houses)
Thus,
QP = 10/12 + 5(0, 1, 2) + 3(0, 1, 2, 3)
Using conditions (1) and (2),
- 24 = 10 + 5 × 1 + 3 × 3
- 15 = 10 + 5 × 1 + 3 × 0 or 15 = 12 + 5 × 0 + 3 × 1
In Block XX, the highest quoted price is Rs. 24 lakh.
Hence, B1, A2, and C2 are occupied, while A1, B2, and C1 are vacant (i.e., available for sale).
Step 2:
From condition (3), E1 and E2 are vacant.
Also, from conditions (2) and (3), exactly one of D1 and F1 is occupied.
For E1,
Quoted Price = 15
= 12 + 5 × 0 + 3 × 1
Therefore, by condition (4), E1 is the only house in Block YY with a parking space.
Further, from condition (3), each of Column D and Column F contains at least one occupied house.
This gives two possibilities:
- If D1 is occupied, then F2 must also be occupied, while D2 may be either occupied or vacant.
- If F1 is occupied, then D2 must be occupied, while F2 may be either occupied or vacant.
House E1 in Block YY has parking space.
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 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.
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 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.
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.
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.
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 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.
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.
The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are placed in ten slots of the following grid based on the conditions below.
1. Numbers in any row appear in an increasing order from left to right.
2. Numbers in any column appear in a decreasing order from top to bottom.
3. 1 is placed either in the same row or in the same column as 10.
4. Neither 2 nor 3 is placed in the same row or in the same column as 10.
5. Neither 7 nor 8 is placed in the same row or in the same column as 9.
6. 4 and 6 are placed in the same row.
What is the row number which has the least sum of numbers placed in that row?
Step 1:
Since 10 is the largest number, it must occupy the cell in Row 1, Column 4.
Also, 2 and 3 cannot lie in the same row or column as 10.
Now consider the placement of 9, the next largest number. It can be placed either in Row 1, Column 3 or Row 2, Column 4.
Step 2:
Assume 9 is placed in Row 2, Column 4.
In that case, 8 and 7 cannot share the same row or column with 9, forcing them into fixed positions.
However, this arrangement leads to a contradiction.
If 4 and 6 are placed in Row 2, there is no valid position left for 2 and 3.
On the other hand, if 4 and 6 are placed in Row 3, the entries in Column 3 will no longer be in decreasing order from top to bottom.
Hence, this case is not feasible.
Step 3:
Therefore, 9 must be placed in Row 1, Column 3.
Consequently, 8 and 7 cannot be in the same row or column as 9, which fixes their positions.
If 4 and 6 are placed in Row 2, there is no valid location available for 2 and 3.
Hence, 4 and 6 must be placed in Row 1.
The final arrangement is:
- Row 1: 4, 6, 9, 10
- Row 2: 2/3, 5, 8
- Row 3: 3/2, 7
- Row 4: 1
Which of the following statements MUST be true?
I. 10 is placed in a slot in Row 1.
II. 1 is placed in a slot in Row 4.
Only I
Both I and II
Only II
Neither I nor II
Both I and II
Step 1:
Since 10 is the largest number, it must occupy the cell in Row 1, Column 4.
Also, 2 and 3 cannot lie in the same row or column as 10.
Now consider the placement of 9, the next largest number. It can be placed either in Row 1, Column 3 or Row 2, Column 4.
Step 2:
Assume 9 is placed in Row 2, Column 4.
In that case, 8 and 7 cannot share the same row or column with 9, forcing them into fixed positions.
However, this arrangement leads to a contradiction.
If 4 and 6 are placed in Row 2, there is no valid position left for 2 and 3.
On the other hand, if 4 and 6 are placed in Row 3, the entries in Column 3 will no longer be in decreasing order from top to bottom.
Hence, this case is not feasible.
Step 3:
Therefore, 9 must be placed in Row 1, Column 3.
Consequently, 8 and 7 cannot be in the same row or column as 9, which fixes their positions.
If 4 and 6 are placed in Row 2, there is no valid location available for 2 and 3.
Hence, 4 and 6 must be placed in Row 1.
The final arrangement is:
- Row 1: 4, 6, 9, 10
- Row 2: 2/3, 5, 8
- Row 3: 3/2, 7
- Row 4: 1
Which of the following statements MUST be true?
I. 2 is placed in a slot in Column 2.
II. 3 is placed in a slot in Column 3.
Both I and II
Neither I nor II
Only II
Only I
Neither I nor II
Step 1:
Since 10 is the largest number, it must occupy the cell in Row 1, Column 4.
Also, 2 and 3 cannot lie in the same row or column as 10.
Now consider the placement of 9, the next largest number. It can be placed either in Row 1, Column 3 or Row 2, Column 4.
Step 2:
Assume 9 is placed in Row 2, Column 4.
In that case, 8 and 7 cannot share the same row or column with 9, forcing them into fixed positions.
However, this arrangement leads to a contradiction.
If 4 and 6 are placed in Row 2, there is no valid position left for 2 and 3.
On the other hand, if 4 and 6 are placed in Row 3, the entries in Column 3 will no longer be in decreasing order from top to bottom.
Hence, this case is not feasible.
Step 3:
Therefore, 9 must be placed in Row 1, Column 3.
Consequently, 8 and 7 cannot be in the same row or column as 9, which fixes their positions.
If 4 and 6 are placed in Row 2, there is no valid location available for 2 and 3.
Hence, 4 and 6 must be placed in Row 1.
The final arrangement is:
- Row 1: 4, 6, 9, 10
- Row 2: 2/3, 5, 8
- Row 3: 3/2, 7
- Row 4: 1
For how many slots in the grid, placement of numbers CANNOT be determined with certainty?
Step 1:
Since 10 is the largest number, it must occupy the cell in Row 1, Column 4.
Also, 2 and 3 cannot lie in the same row or column as 10.
Now consider the placement of 9, the next largest number. It can be placed either in Row 1, Column 3 or Row 2, Column 4.
Step 2:
Assume 9 is placed in Row 2, Column 4.
In that case, 8 and 7 cannot share the same row or column with 9, forcing them into fixed positions.
However, this arrangement leads to a contradiction.
If 4 and 6 are placed in Row 2, there is no valid position left for 2 and 3.
On the other hand, if 4 and 6 are placed in Row 3, the entries in Column 3 will no longer be in decreasing order from top to bottom.
Hence, this case is not feasible.
Step 3:
Therefore, 9 must be placed in Row 1, Column 3.
Consequently, 8 and 7 cannot be in the same row or column as 9, which fixes their positions.
If 4 and 6 are placed in Row 2, there is no valid location available for 2 and 3.
Hence, 4 and 6 must be placed in Row 1.
The final arrangement is:
- Row 1: 4, 6, 9, 10
- Row 2: 2/3, 5, 8
- Row 3: 3/2, 7
- Row 4: 1
What is the sum of the numbers placed in Column 4?
Step 1:
Since 10 is the largest number, it must occupy the cell in Row 1, Column 4.
Also, 2 and 3 cannot lie in the same row or column as 10.
Now consider the placement of 9, the next largest number. It can be placed either in Row 1, Column 3 or Row 2, Column 4.
Step 2:
Assume 9 is placed in Row 2, Column 4.
In that case, 8 and 7 cannot share the same row or column with 9, forcing them into fixed positions.
However, this arrangement leads to a contradiction.
If 4 and 6 are placed in Row 2, there is no valid position left for 2 and 3.
On the other hand, if 4 and 6 are placed in Row 3, the entries in Column 3 will no longer be in decreasing order from top to bottom.
Hence, this case is not feasible.
Step 3:
Therefore, 9 must be placed in Row 1, Column 3.
Consequently, 8 and 7 cannot be in the same row or column as 9, which fixes their positions.
If 4 and 6 are placed in Row 2, there is no valid location available for 2 and 3.
Hence, 4 and 6 must be placed in Row 1.
The final arrangement is:
- Row 1: 4, 6, 9, 10
- Row 2: 2/3, 5, 8
- Row 3: 3/2, 7
- Row 4: 1
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