CAT 2025 Lesson : Arrangements - Cases 1 to 3

1) Persons X, Y, Z and Q live in red, green, yellow or blue-coloured houses placed in a sequence on a street. Z lives in a yellow house. The green house is adjacent to the blue house. X does not live adjacent to Z. The yellow house is in between the green and red houses. The colour of the house, X lives in is
[CAT 2000]

(1) blue
(2) green
(3) red
(4) Not possible to determine

Solution

“Persons X, Y, Z and Q live in red, green, yellow or blue-coloured houses placed in a sequence on a street.” From this statement, we can infer that this is a Linear Arrangement case.

Clue 1: “Z” lives in the yellow house, this is a direct clue.

Clue 2: the green house is adjacent to the blue house. This clue has two possibilities as the order isn't specified. The two possibilities are:
(i) (Green, Blue)
(ii) (Blue, Green)

Clue 3: “X” does not live adjacent to “Z”. From this clue, we can say, “X” is not to the immediate left or right of “Z” in other words “X” is not the immediate neighbour of “Z”.

Clue 4: The yellow house is in between the green and red house. Since the order of the green and red house is not given, there are two possibilities with this clue:
(i) (Green, Yellow, Red)
(ii) (Red, Yellow, Green)

Case Solution

From clues 2 and 4, we can conclude the green house cannot be the first or the last house in the sequence.

If green was the first house, blue has to be the second house (from clue 2) but yellow should be in-between the green and red house. (from clue 4) Similarly, green cannot be the last house either as it does not satisfy both clue 2 and clue 4.

Hence the green house is either the 2nd or the 3rd house in the sequence. Based on this we get two different cases:

Case 1:



Case 2:



From clue 3, “X” is not the immediate neighbour of “Z”. Hence, from cases 1 and 2 we can conclude that “X” cannot be living in Red and Green coloured houses.

Case 1:



Case 2:



Hence from both the cases, we can conclude that X lives in the Blue house.

Answer: (1) blue

2) Six persons are playing a card game. Suresh is facing Raghubir who is to the left of Ajay and to the right of Pramod. Ajay is to the left of Dhiraj. Yogendra is to the left of Pramod. If Dhiraj exchanges his seat with Yogendra and Pramod exchanges with Raghubir, who will be sitting to the left of Dhiraj?
[CAT 2002]

(1) Yogendra
(2) Raghubir
(3) Suresh
(4) Ajay

Solution

From “Suresh is facing Raghubir”, we can infer that this cannot be a linear type arrangement case. Hence, it is a closed arrangement case and for simplicity let us consider it as a circular arrangement case.

Let us number the seat at the table for identification purposes.



If Suresh sits at seat 4, Raghubir sits at the seat directly opposite to him, which is seat 1.
Since Raghubir sits to the left of Ajay and right of Pramod , seats 6 and 2 are taken by Ajay and Pramod respectively.



Yogendra and Dhiraj are remaining.
It is given that Yogendra is seated to the left of Pramod. The seat vacant to the left of Pramod is seat 3. Thus the remaining seat 5 is taken by Dhiraj.



If Dhiraj exchanges his seat with Yogendra, Dhiraj sits at seat 3 and Yogendra at seat 5.
Further, if Pramod exchanges his seat with Raghubir, their new seats will be 1 and 2 respectively.

Hence the new seating arrangement in ascending order is: 1-Pramod, 2-Raghubir,3-Dhiraj, 4-Suresh, 5-Yogendra, 6-Ajay.



The person to the left of Dhiraj in the new arrangement is Suresh.

Answer: (3) Suresh

3) Children are in pursuit of a dog whose leash has broken. Krishnarajan is directly behind the dog. Rangarajan is behind Krishnarajan. Natrajan is behind Rangarajan. Premrajan is ahead of the dog walking down the street in the opposite direction. As the children and dog pass, Premrajan turns around and joins the pursuit. He runs in behind Rangarajan. Krishnarajan runs faster and is alongside the dog on the left. Rangarajan runs faster and is alongside the dog on the right. Which child is directly behind the dog?
[XAT 2009]

(1) Krishnarajan
(2) Rangarajan
(3) Natrajan
(4) Premrajan
(5) None of above

Solution

Let us assume the dog is moving north and the children are following the dog.

The order of the children following the dog based on the proximity to the dog is – Krishnarajan who is just behind the dog, followed by Rangarajan who is behind Krishnarajan and finally Natrajan who is behind Rangarajan.

Premrajan is ahead of the dog but is facing south which is opposite to the direction of the dog running towards.



The dog and children pass Premrajan who then joins the queue of boys following the dog.

The new order of following the dog based on proximity is – Krishnarajan-Rangarajan-Premrajan-Natrajan.



Krishnarajan ad Rangarajan run faster and catch up with the dog and take their places to the left and right alongside the dog respectively.

The speeds of Natrajan and Premrajan are not mentioned. There is also no mention of any further order change. Therefore, based onthe previous order, Premrajan is closer to the dog than Natrajan.

Hence, Premrajan must be the child right behind the dog.



Answer: (4) Premrajan