Practice Questions: Team Formation- 1 | Logical Reasoning (LR) and Data Interpretation (DI) - CAT PDF Download

Direction: A team of teachers has to be chosen out of the eight available teachers to represent the university at the Syllabus Council meet. The eight teachers are Rawat, Abhishek, Vinod, Tarun, Kapil, Shalini, Vatsala and Prateek. The selection must follow the additional conditions:
(i) The team must have a minimum of four members.
(ii) If Rawat is selected, then Vatsala has to be definitely selected.
(iii) Exactly one from Prateek or Tarun has to be selected.
(iv) Shalini and Rawat cannot be selected together.
(v) Kapil and Shalini have to be selected together.

Q1: If Rawat is a member of a team of four members, in how many ways can the team be selected?
(a) Two
(b) Three
(c) Four
(d) Five
Ans: (c)
Sol: If Rawat is selected, Shalini cannot be selected, and therefore Kapil also cannot be selected. Further, Vatsala is definitely selected. Exactly one from Prateek or Tarun has to be selected. This can happen in two ways. Now, the fourth member can be any one from Abhishek and Vinod, which can happen in two ways. Therefore, the total number of ways = 2 x 2 = 4 ways.

Q2: If Shalini is selected, what can be the maximum number of members in the team?
(a) Five
(b) Six
(c) Four
(d) Seven
Ans: (b)
Sol: If Shalini is selected, Rawat is definitely not selected. Also, exactly one from Prateek or Tarun is selected, that is, the team can have a maximum of six members.

Q3: Who cannot be a member of a team of six members?
(a) Kapil
(b) Tarun
(c) Abhishek
(d) Rawat
Ans: (d)
Sol: If Rawat is selected, Shalini cannot be selected. Also, Shalini and Kapil will be selected together. Therefore, if Shalini is not selected, Kapil will also not be selected. It is mentioned that exactly one from Prateek or Tarun will be selected. Taking all the conditions into consideration, Rawat cannot be a member of a team having six members.

Direction: A group of four nations has to be selected out of eight members of the Security Council consisting of the United States, France, Japan, India, China, Germany, the United Kingdom and Sri Lanka. While India, China, Japan, and Sri Lanka are from Asia, the other countries are from the rest of the world. further conditions are as follows:
(i) Out of the four countries, at least one country each must be from Asia and rest of the World. Further, the group must include at least one from India and the United States.
(ii) If Sri Lanka is chosen, neither France nor Germany can be chosen.
(iii) If China is chosen, exactly one from the United States or the United Kingdom has to be chosen.
(iv) If japan is chosen, India cannot be the chosen country.

Q4: If there are two countries chosen from the rest of the world, which of the following combinations is not possible for the countries chosen from Asia?
(a) India, China
(b) India, Sri Lanka
(c) China, Sri Lanka
(d) Japan, China
Ans: (c)
Sol: If China and Sri Lanka are the two countries chosen from Asia, then only one from the UK or USA can be selected (condition 3). Also, if Sri Lanka is chosen, neither France nor Germany can be selected. Therefore, it is not possible to select China and Sri Lanka as the two countries from Asia.

Q5: If the United Kingdom is the only country chosen from the rest of the world, which country is definitely not chosen from Asia?
(a) India
(b) Sri Lanka
(c) China
(d) Japan
Ans: (d) Japan
Sol: India has to be definitely selected; therefore, Japan cannot be selected.

Direction: A team of teachers has to be chosen out of the eight available teachers to represent the university at the Syllabus Council meet. The eight teachers are Rawat, Abhishek, Vinod, Tarun, Kapil, Shalini, Vatsala and Prateek. The selection must follow the additional conditions:
(i) The team must have a minimum of four members.
(ii) If Rawat is selected, then Vatsala has to be definitely selected.
(iii) Exactly one from Prateek or Tarun has to be selected.
(iv) Shalini and Rawat cannot be selected together.
(v) Kapil and Shalini have to be selected together.

Q6: Which among the following is not an acceptable combination?
(a) Rawat, Vinod, Abhishek, Tarun, Vatsala
(b) Vinod, Abhishek, Prateek, Vatsala, Tarun
(c) Shalini, Kapil, Vatsala, Tarun
(d) Tarun, Vatsala, Shalini, Kapil, Vinod, Abhishek
Ans: (b)
Sol:  The team given in option (b) is not possible since Shalini and Kapil have to be selected together. 

Q7: Who among the following cannot be members of the same team?
(a) Rawat, Vinod
(b) Kapil, Abhishek
(c) Kapil, Rawat
(d) Vatsala, Vinod
Ans: (c)
Sol: Kapil and Rawat cannot be members of the same team since Kapil and Shalini are to be always selected together, while Rawat and Shalini can never be selected in the same team.