Example Case 3

Directions for questions 4 to 6: Answer the questions based on the passage below.

A group of three or four has to be selected from seven persons. Among the seven are two women: Fiza and Kavita, and five men: Ram, Shyam, David, Peter and Rahim. Ram would not like to be in the group if Shyam is also selected. Shyam and Rahim want to be selected together in the group. Kavita would like to be in the group only if David is also there. David, if selected, would not like Peter in the group. Ram would like to be in the group only if Peter is also there. David insists that Fiza be selected in case he is there in the group.
[CAT 2001]

4) Which of the following is a feasible group of three?

(1) David, Ram and Rahim
(2) Peter, Shyam and Rahim
(3) Kavita, David and Shyam
(4) Fiza, David and Ram

5) Which of the following is a feasible group in four?

(1) Ram, Peter, Fiza and Rahim
(2) Shyam, Rahim, Kavita and David
(3) Shyam, Rahim, Fiza and David
(4) Fiza, David, Ram and Peter

6) Which of the following statements is true?

(1) Kavita and Ram can be part of a group of four
(2) A group of four can have two women
(3) A group of four can have all four men
(4) None of these

Solution

4)
Let us consider option 1: David, Ram and Rahim
If Rahim is selected, then Shyam should be selected (Condition 2). Shyam and Ram can't be selected together (condition 1). Hence, option 1 is rejected.

Option 2: Peter, Shyam and Rahim
Shyam and Rahim are selected. Peter can be selected and here is no violation in the conditions given. Hence option 2 is okay.

Option 3: Kavita, David and Shyam
Kavitha and David are selected. If David is selected, then Fiza should be selected (Condition 6). Hence, option 3 is rejected.

Option 4: Fiza, David and Ram
Fiza and David are selected. If Ram is selected, then Peter should be selected. That increases the group count to four which is rejected.

Hence, option 2 is the answer.

Answer: 4) (2) Peter, Shyam and Rahim

5)
Let '$W \varpropto X$' mean W and X cannot be together, 'W / X' means W or X and 'W & X' means that if W is selected then X is also selected respectively. The case details can be written as follows.

Men: Ram, Rahim, Peter, David, Shyam
Women: Fiza, Kavitha
Notes:
1. $Ram\varpropto Shyam$
2. 'Shyam & Rahim' or 'Rahim & Shyam'
3. 'Kavitha & David'
4. $David \varpropto Peter$
5. 'Ram & Peter'
6. 'David & Fiza'
Let us consider option 1: Ram, Peter, Fiza and Rahim
If Rahim is selected, then Shyam is also selected. Thus, option 1 is rejected.

Option 2: Shyam, Rahim, Kavita and David
If Shyam is selected, then Rahim is also selected. If Kavitha is selected, then David is also selected. If David is selected, then Fiza should be selected (Condition 6). Thus option 2 is rejected.

Option 3: Shyam, Rahim, Fiza and David
If Shyam is selected, then Rahim is also selected. If David is selected, then Fiza is also selected. Thus option 3 is accepted.

Option 4: Fiza, David, Ram and Peter
If David is selected, then Peter cannot be selected. Thus option 4 is rejected.

Hence, option 2 is the answer.

Answer: (3) Shyam, Rahim, Fiza and David;

6)
Let' $W \varpropto X$' mean W and X cannot be together, 'W / X' means W or X and 'W & X' means that if W is selected then X is also selected respectively. The case details can be written as follows.

Men: Ram, Rahim, Peter, David, Shyam
Women: Fiza, Kavitha
Notes:
1. $Ram\varpropto Shyam$
2. 'Shyam & Rahim' or 'Rahim & Shyam'
3. 'Kavitha & David'
4. $David \varpropto Peter$
5. 'Ram & Peter'
6. 'David & Fiza'
Let us consider option 1: Kavita and Ram can be part of a group of four

If Kavitha is selected, then David is also selected. If David is selected, then Fiza is also selected. If ram is selected, then Peter is also selected. Hence a group of four cannot be formed.

Option 2: A group of four can have two women

If Fiza and Kavitha are selected, then a group of only 3 can be formed.
Since Kavitha is selected, then David is also selected. David and Peter cannot be selected together. Since Peter is not selected, Ram cannot be selected. Shyam and Rahim also cannot be selected.

Option 3: A group of four can have all four men

Since both the women are not selected David cannot be selected ('Kavitha & David'). Ram and Shyam cannot be selected together (). Hence, a group of three or less can only be formed.

Hence option 4 is the answer.

Answer: (4) None of these

Answer:
4) (2) Peter, Shyam and Rahim
5) (3) Shyam, Rahim, Fiza and David
6) (4) None of these

Example Case 4

Instructions for questions 7 to 9: Questions are based on a set of conditions. In answering some of the questions, it may be useful to draw a rough diagram. Choose the response that most accurately and completely answers each question.

In a local pet store, seven puppies wait to be introduced to their new owners. The puppies, named Ashlen, Blakely, Custard, Daffy, Earl, Fala and Gabino, are all kept in two available pens. Pen 1 holds three puppies, and pen 2 holds four puppies.

If Gabino is kept in pen 1, then Daffy is not kept in pen 2.
If Daffy is not kept in pen 2, then Gabino is kept in pen 1.
If Ashlen is kept in pen 2, then Blakely is not kept in pen 2.
If Blakely is kept in pen 1, then Ashlen is not kept in pen 1.
[XAT 2010]

7) Which of the following groups of puppies could be in pen 2?

(1) Gabino, Daffy, Custard, Earl.
(2) Blakely, Gabino, Ashlen, Daffy.
(3) Ashlen, Gabino, Earl, Custard.
(4) Blakely, Custard, Earl, Fala.
(5) Gabino, Ashlen, Fala, Earl.

8) If Earl shares a pen with Fala, then which of the following MUST be true?

(1) Gabino is in pen 1 with Daffy.
(2) Custard is in pen 2.
(3) Blakely is in pen 2 and Fala is in pen 1.
(4) Earl is in pen 1.
(5) Gabino shares a pen with Blakely.

9) If Earl and Fala are in different pens, then which of the following must NOT be true?

(1) Fala shares a pen with Custard.
(2) Gabino shares a pen with Ashlen.
(3) Earl is in a higher-numbered pen than Blakely.
(4) Blakely shares pen 2 with Earl and Daffy.
(5) Custard is in a higher-numbered pen than Fala.

Solution

7)
Let '$W \varpropto X$' mean W and X cannot be together, 'W / X' means W or X and 'W & X' means that if W is selected, then X is also selected respectively. The case details can be written as follows.

Let us call the puppies Ashlen, Blakely, Custard, Daffy, Earl, Fala and Gabino as A, B, C, D, E, F & G respectively.

Given that pen 1 has three puppies and pen 2 has four puppies.

Notes:

(Conditions given)
1 & 2 state that G & D together can either be in P1 or P2 (G, D)
3 & 4 state that if A is in Pen 1 then B is in Pen 2 or Vice versa. ($A \varpropto B$)
Based on the conditions given in the notes, we can directly eliminate options 2, 3 & 5.
In option 1, $A \varpropto B$ means either A or B should be present in pen 2. Hence option 1 is also rejected.

Thus option 4 is the answer.

Answer: 7) (4) Blakely, Custard, Earl, Fala.

8)
Let '$W \varpropto X$' mean W and X cannot be together, 'W / X' means W or X and 'W & X' means that if W is selected, then X is also selected respectively. The case details can be written as follows.

Let us call the puppies Ashlen, Blakely, Custard, Daffy, Earl, Fala and Gabino as A, B, C, D, E, F & G respectively.

Given that pen 1 has three puppies and pen 2 has four puppies.

Notes:

(Conditions given)
1 & 2 state that G & D together can either be in P1 or P2 (G, D)
3 & 4 state that if A is in Pen 1 then B is in Pen 2 or Vice versa. ($A \varpropto B$)

As given, E & F are kept in a pen and A or B should be with them ($A \varpropto B$).

If (G & D) are kept with E, F, (A/B), then total puppies will be five which is rejected. Thus (G & D) are kept in the other pen.

The puppy C can either be in both the pens and that decides whether the pen is Pen 1 Or Pen 2.

On considering the options,
Option 2: Custard (C) is in pen 2 is true and it is Pen 2.

Answer: (2) Custard is in pen 2.

9)
Let '$W \varpropto X$' mean W and X cannot be together, 'W / X' means W or X and 'W & X' means that if W is selected, then X is also selected respectively. The case details can be written as follows.

Let us call the puppies Ashlen, Blakely, Custard, Daffy, Earl, Fala and Gabino as A, B, C, D, E, F & G respectively.

Given that pen 1 has three puppies and pen 2 has four puppies.

Notes:

(Conditions given)
1 & 2 state that G & D together can either be in P1 or P2 (G, D)
3 & 4 state that if A is in Pen 1 then B is in Pen 2 or Vice versa. ($A \varpropto B$)

As given, E & F are kept in different pens and A or B should be with them($A \varpropto B$).

(G & D) should be kept together. Thus they can be in both the pens. Based on (G & D)'s position, C's pen is decided.

Consider option 1: F shares a pen with C which is a possible conclusion. Hence option 1 is rejected.

Option 2: G shares a pen with A which is a possible conclusion. Hence, option 2 is rejected.

Option 3: E is in a higher-numbered pen than B is false as B and E can be kept in a pen which has a total of three puppies.

Hence, option 3 is the answer.

Answer: (5) Custard is in a higher-numbered pen than Fala.

Answer:
7) (4) Blakely, Custard, Earl, Fala
8) (2) Custard is in pen 2
9) (5) Custard is in a higher-numbered pen than Fala