Important Concepts: Team Formations | Logical Reasoning (LR) and Data Interpretation (DI) - CAT PDF Download

Introduction

• Visualization of Team Structure: Essential skill involves picturing the arrangement of people or objects in teams, including the determination of the number of individuals or elements in each team.
• Ordering Clues Correctly: Skill in prioritizing and arranging clues in the logical sequence outlined in the theory of logical reasoning. Establishing the correct order of usage aids in systematic problem-solving.

• Symbolic Representation Creation: Proficiency in creating symbolic representations of the given clues. This enables the consolidation of relevant information while forming teams, making it easier to identify connections and constraints.
• Effective Utilization of Indirect Clues: Skill in recognizing the appropriate moment during problem-solving to leverage indirect clues provided in the question. Waiting for the right context ensures optimal utilization of information for forming teams.
• Logical Reasoning Theory Application: Application of principles from the theory of logical reasoning, emphasizing the importance of correct sequencing of clues and symbolic representation creation.
• Patient Problem-Solving Approach: Ability to exercise patience and strategic waiting for the opportune moment in the problem-solving process, allowing for the effective use of indirect clues.
• Team Formation Constraints: Recognition of constraints and conditions related to certain individuals who must be placed together or cannot be part of the same team.
• Application of Symbolic Representation: Proficient use of symbolic representations to consolidate information, aiding in the creation and understanding of team formations as per the given conditions.
• Strategic Problem-Solving: Skill in strategic thinking during the problem-solving process, ensuring that each clue is appropriately considered and applied to facilitate the formation of teams.
• Logical Approach to Constraints: Logical approach to constraints, considering the implications and limitations outlined in the question while forming teams.

Understanding Keywords

1. At least one element — This means one or more than one. We can denote it as 1+ when noting down the clauses.

2. At most one element — It means maximally one, that is, either zero or one. We can denote it as 0/1.

3. At most two elements — It means maximally two, that is, zero, one, or two. We denote it as 0/1/2.

4. If you select A, then you also have to select B. 

We can draw the following inferences from the above statement:

(a) If A is selected, B has to be selected.

(b) No case is possible where A is selected and B is not selected.

(c) A case is possible where B is selected, but A may or may not be selected.

(d)  If B is not selected, then we can conclude A is also not selected, consequently.

5. Only if A happens then B happens. 

We can draw the following inferences from the above statement:

(a) B is selected only when A is selected.

(b) B is not selected when A is not selected.

6. Either you can select A or B. 

We can draw the following inferences from the above statement:

(a) B has happened, but now A cannot happen.

(b) A has happened, but now B cannot happen.

Let's understand with an example:

Three adult women (R, S, and T), two adult men (U and V), and four children (W, X, Y, and Z) are going to watch a movie. Though, during the online booking of the tickets, they realized that the nine seats available for the show are in three different classes —Silver Class, Gold Class and Lounge. The layout also showed that in each class, three adjacent seats are available.
To watch the movie, they decide to have the three groups of three members each as per the following conditions:
No adults of the same gender can be together in One group.
W cannot be in R’s group.
X must be in a group with S or U, or both.

1. If R is the only adult in one group, the other members of her group must be
(a) W and Y
(b) X and Y
(c) X and Z
(d) Y and Z
2. Which of the following pairs of people can be in the same group as W?
(a) R and Y
(b) S and U
(c) S and V
(d) U and V
3. Any of the following pairs of people could be in a group with X, except:
(a) R and U
(b) S and T
(c) S and U
(d) S and W
Solution:
According to the rules, W and R cannot be in the same group. No two adults of the same gender can be in the group strictly. Consequently, no group can be formed using R and U, R and V, S and U, S and V, T and U, and T and V.
Addressing Question 1, option (a) is not possible since as per the clause given W cannot be in R’s group. In the same way, Option (b) and option (c) is not possible since as per the clause given X must be in a group with S or U or both. Option (d) is correct as it remains after eliminating the other options and it follows the rules given.
Addressing Question 2, option (a) is not possible since W cannot be in R’s group. Likewise, Option (b) is incorrect because at least either S or U  must be in group with X. Option (d) is incorrect because it goes against the rules of the question asked as U and V are two adults of the same gender. Option (c) is correct because neither does the group formed contains two adults of the same gender nor does it go against other rules given.
Addressing Question 3, option (a) is incorrect because it can be in a group with X. Similarly, Option (c) and Option (d) are incorrect because they adhere to the rules given and can be in a group with X. In conclusion, option (b) is correct since the pair of S and T cannot be in a group with X as they are two adults of the same gender.

Solved Examples: Level of Difficulty 1

Directions for Questions 1 to 3:
(i) A home stay has 6 rooms A, B, C, D, E and F. Among these, A and C can accommodate two persons each; the rest can accommodate only one each.
(ii) Eight guests P, Q, R, S, T, U, W and X are to be kept in these rooms. Q, T and X are females while the rest are males. The two sexes can't be put together in the same room. No man is willing to stay in room C or F.
(iii) P wants to be alone but does not want to stay in rooms B or D. S needs a partner but is not ready to stay with U or W. X does not want to share her room.

Q1: Who among the following will stay in room E?
(a) U
(b) W
(c) P
(d) Data inadequate
Ans: (c)

Q2: In which of the following rooms will U stay?
(a) B
(b) D
(c) А
(d) B or D
Ans: (d)

Q3: X will stay in which of the following rooms?
(a) C
(b) F
(c) B
(d) Data inadequate
Ans: (b)
Solutions:
Initial information:
A (2)
B (1)
C (2)
D (1)
E (1)
F (1)
Also, P+, Q, R*, S*, T, U*, W, X. From clue (ii), Room C (2 people) and Room F (1 person) should be women's rooms as men cannot be placed there. From clue (iii P must be in E, S must be in A (where U and W cannot be).
Thus, S must be sharing his room with R. Also, U and W must be in some random order in Rooms B or D. Also, X must be in Room F as she is a female and wants a single room.
Collating all this, we get:
A (2) S, R
B (1)
C (2) Q, T
D (1)
E (1) Р
F (1) X
Hence, the answers are:
1. P (c)
2. B or D (d)
3. F (b)

Solved Examples: Level of Difficulty 2

Directions for Questions 1 to 3: (Constraint Based Selection) A group of three or four has to be selected from seven persons. Among the seven there are two women Fatima and Kaira, and five men-Rahul, Sharan, Dharam, Param and Rai. Rahul would not like to be in the group if Sharan is also selected. Sharan and Rai want to be selected together in the group. Kaira would like to be in the group only if Dharam is also there. Dharam, if selected, would not like Param in the group. Rahul would like to be in the group only if Param is also there. Dharam insists that Fatima must be selected in case he is there in the group.

Q1: Which of the following is a feasible group of three?
(a) Dharam, Rahul, Rai
(b) Param, Sharan, Rai
(c) Kaira, Dharam, Sharan
(d) Fatima, Dharam, Rahul
Ans: (b)

Q2: Which of the following is a feasible group of four?
(a) Rahul, Param, Fatima, Rai
(b) Sharan, Rai, Kaira, Dharam
(c) Sharan, Rai, Fatima, Dharam
(d) Fatima, Dharam, Rahul, Param 
Ans: (c)

Q3: Which of the following statements is true?
(a) Kaira and Rahul can be part of a group of four.
(b) A group of four can have two women.
(c) A group of four can have all four men.
(d) None of the above.
Ans: (d)
Solutions:
Ans 1: First of all summarise the basic information as follows:
Women: Fatima, Kaira
Men: Rahul, Sharan, Dharam, Param and Rai.
Rahul not Sharan.
Sharan+ Rai
Kaira only if Dharam
Dharam does not want Param
Rahul only if Param
Dharam only if Fatima.
After this go through each question through options meeting all the conditions:
Option (a) is rejected as it selects Dharam without Fatima.
Option (c) is rejected for the same reason.
Option (d) is rejected as it selects Rahul without Param. Only Option (b) obeys all conditions.

Ans 2: Only the third group can be seen to be feasible.

Ans 3: Option (a): cannot be true since if Kaira and Rahul are selected, Dharam and Param must also be selected and Dharam wants Fatima as a part of his group. Thus we would not be able to create a group of 4.
Option (b): If Fatima and Kaira are selected, then Dharam has to be part of the group. The fourth person has to be selected from amongst the four men left. However, Rahul, Sharan and Rai have to be selected with at least one more of the 4 males. Also since Dharam is selected, Param cannot be. Thus there is no way to select exactly 4 people in the group.
Option (c): This is also not possible as Dharam wants Fatima so he cannot be selected amongst a selection of 4 males. This means that we must take all the other 4, but Rahul does not want to be in a group with Sharan.
Hence, None of these is true.