Team Formations - Logical Reasoning (LR) and Data Interpretation (DI) - CAT

Team formation questions are another question type which are commonly seen in most exams. The questions consist typically of a group of people/objects that have to be put together in teams— albeit with a set of constraints/conditions about certain people who need to be put together/ cannot be put together in a team.
The key skills involved in solving team formation questions would involve the following:

• The ability to visualize the structure of the teams to be formed including the number of people/objects in each team 
• The ability to order the clues in the correct order of usage (as explained in the theory of logical reasoning) 
• The ability to create symbolic representation of the various clues provided so that you can bring together each of the relevant clues while creating the teams 
• The ability to wait for and reach the appropriate time in the problem solving situation from where the indirect clues provided in the question can be used.

Illustrated below are the solutions to a few typical questions on team formations. We would urge you to first have a look at the questions and try to solve the same on your own before looking at the solutions.

Example 1. Directions: Read the information given below and answer the questions.
A director is casting a movie about twins. Selection must be made from among nine people—Amartya, Bhupesh, Caruna, Divya, Elangovan, Farly, Girish, Harish, and Isha. Amartya is Bhupesh’s twin, Caruna is Divya’s twin, and Elangovan is Farly’s twin. Girish, Harish and Isha may each be selected only as “extras.”

• At least two pairs of twins must be selected.
• At least as many women as men must be selected.
• Amartya and Bhupesh must both be selected if either is selected.
• Caruna and Divya both must be selected if either is selected.
• Elangovan and Farly need not both be selected.
• At least one “extra” must be selected.
• Amartya, Bhupesh, Elangovan, Girish and Harish are men.

(i) Which of the following is an acceptable cast for the movie?
(a) Amartya, Bhupesh, Elangovan, Farly, Isha
(b) Caruna, Divya, Farly, Girish, Harish, Isha
(c) Bhupesh, Caruna, Divya, Elangovan, Harish, Isha
(d) Caruna, Divya, Elangovan, Farly, Girish, Harish, Isha

(ii) Which of the following people must be included in the cast?
(a) Divya
(b) Isha
(c) Farly
(d) Harish

To solve this we will create a diagram where men will be denoted by upper case letters and women with lower case letters and we will list the extras separately to avoid confusion. Here given that Caruna and Divya must both be selected because if they were not selected then Amartya and Bhupesh or Elangovan and Farly ( three of whom are men) would all be selected; as a result only two women Farly and Isha at most will be selected. However, according to the constraints at least as many women as men must be selected, thus Caruna and Divya must both be selected.

(i) Eliminate each options using the clues given in the information. Only option (d) suffices. Hence option (d) is the correct answer.
(ii) Caruna and Divya must both be selected. Hence option (a) is the correct answer.

Example 2. Read the information given below and answer the questions.
Vijayshree wants to take four courses this trimester. There are only seven courses in which she is interested: three marketing courses — Distribution, Advertising and PR; and four Finance courses— International Finance, Accounting, Corporate Finance and Financial Services. To meet college requirements she must take two marketing courses. There are some scheduling problems: International Finance overlaps both Advertising and Corporate Finance but she can choose Advertising and Corporate Finance as two different courses. Distribution is given at the same time as Accounting.
(i) If Vijayshree decides she will take International Finance, what will her other three courses be? 
(a) Distribution, PR and Advertising
(b) Distribution, PR and Financial Services
(c) Distribution, PR and Accounting
(d) PR, Advertising and Financial Services

(ii) If Vijayshree takes four courses this trimester, then which of the following statement is not possible?
I. She takes Accounting and does not take Advertising. 
II. She takes Corporate Finance and does not take Advertising. 
III. She takes International Finance and does not take PR.
(a) I only
(b) II only
(c) III only
(d) I and III only

(iii) Which of the following must always be true? 
I. Vijayshree must take PR if she takes Corporate Finance. 
II. Vijayshree must take Advertising if she takes Accounting. 
III. Vijayshree must take Accounting if she takes Advertising. 
(a) I, II, and III
(b) II, and III only
(c) I and II only
(d) II only

(i) It can be seen that if she takes International Finance, she would not be able to take the Advertising and Corporate Finance course. This means that she has to choose Distribution and PR as her two marketing courses and because Distribution overlaps with Accounting, her second finance course must be Financial Services. Option (b) is correct. 

(ii) Statement I is definitely not possible because if she takes Accounting she cannot take Distribution and she must have to take Advertising.
Statement II is possible, while statement III can be seen to not be possible as if she takes International Finance she has to take PR as Advertising would not be available to her.
Option (d) is correct. 

(iii) Statement I is not necessarily true as if she takes Corporate Finance she can take up Distribution and Advertising and skip PR, i.e., PR is not necessary if she has taken Corporate Finance.
Statement II is mandatorily true because if she takes Accounting, she cannot take Distribution and hence she would be forced to take up Advertising as one of her two compulsory marketing courses. Statement III is not necessarily true.
Thus option (d) is correct.