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CAT 2025 Lesson : Selections - Introduction
1. Introduction
Selections questions deal with the selection of a team of people from a larger consideration set. We will usually be given a group of people such as students, sport-persons, etc and a set of conditions. For instance, both A and B must be part of the team, if P is selected then Q must also be selected, only one of X and Y can be in the team, exactly one of R and S must be in the team, etc. The conditions can also be rules such as – a cricket team must have 5 batsmen, 3 bowlers, 2 all-rounders and 1 wicket keeper; a quiz team must carry at least an expert in science, spelling, maths; a coding team must have at least 3 Indians, 2 Koreans and 1 American OR a coding team must have at least 2 coders proficient in Java, 3 coders proficient in SQL and 2 coders proficient in Python.These questions are fairly common in all MBA entrance tests, and are usually quick solving ones. They do test our logic and you have to be careful to read and understand the exact meaning of the information given.
The teams can be a bit flexible here, and we may not be able to find the exact team. The questions will also reflect this, and many questions are if-then variants (if P is on the team, then which of the following people will definitely not be on the team).
Let us solve a few questions to clarify this further.
Concept Case 1
A team of 4 students are to be selected from a group of 8 students - A, B, C, D, E, F, G and H - to represent a school in a quiz competition. The following conditions must be met while selecting the team.
1) If C is selected, then D has to be selected.
2) If A is selected, then F cannot be selected.
3) Exactly one of E or G has to be selected.
4) B and H are friends and, therefore, if one of them is selected, then the other should also be selected.
1) If H is selected, then who among the following cannot be selected?
(1) D
(2) C
(3) G
(4) A
2) If E and F are selected, then who among the following can be the other 2 persons selected?
(1) A, D
(2) B, D
(3) C, D
(4) None of these
3) If A and D are selected, then who among the following can definitely not be selected?
(1) C
(2) E
(3) G
(4) B
4) In how many different ways can the team be selected?
B, H, E, A
B, H, E, F
B, H, E, D
B, H, G, A
B, H, G, F
B, H, G, D
E, C, D, A
E, C, D, F
G, C, D, A
G, C, D, F
Solution
1)Let '' mean W and X cannot be together, 'W / X' means W or X ,'W & X' means If W is selected then X is also selected respectively . The case details can be written as follows.
Notes:
{Conditions given}
1. C & D
2. ''
3. Exactly 1 of E, G
4. B & H
The question states that if H is selected then B should be selected. [Condition 4].
As exactly one of E, G need to be selected, [Condition 3].
As A and F cannot be selected together, A/F need to be selected [Condition 2].
If C is selected, then D should be selected that makes a total of 5 members in a team which is not needed. But D alone can be selected by replacing A/F.
So, there are two cases possible where H is selected in each of the cases.
C is definitely not selected.
Answer: (2) C
2)
Let '' mean W and X cannot be together, 'W / X' means W or X, 'W & X' means If W is selected then X is also selected respectively . The case details can be written as follows.
Notes:
{Conditions given}
1. C & D
2. ''
3. Exactly 1 of E, G
4. B & H
The question states E and F are selected then , Based on conditions 2 & 3
Based on conditions 1 & 4
From the options given, 'C, D' is the answer.
Answer: (3) C, D
3)
As stated, if A and D are selected then based on condition 1, F cannot be selected.
From condition 3, either E or G is selected
If B is selected, then H is also selected. That gives us a total of 5 students, which is not needed. This leaves us with C who needs to be selected.
B is not definitely selected.
Answer: (4) B
4)
Notes:
{conditions given}
1. C & D
2. ''
3. Exactly 1 of E, G
4. B & H
As the question states, we need to find number of possible teams based on the given conditions.
Case 1:
If B is selected, then H has to be selected. If A is selected then F cannot be selected. Exactly one from E/G should be selected, which gives us two possibilities.
1. B, H, E, A
2. B, H, G, A
Case 2:
If B is selected then H has to be selected. If F is selected then A cannot be selected. Exactly from E/G, one should be selected, which gives us two possibilities.
3. B, H, E, F
4. B, H, G, F
Case 3:
If B is selected then H is selected. D can be selected. Exactly one from E/G should be selected, which gives us two possibilities.
5. B, H, E, D
6. B, H, G, D
Case 4:
From E/G, exactly one should be selected which is E. Based on condition 1, both C & D are selected. A & F can't be selected together, which gives us two possibilities.
7. E, C, D, A
8. E, C, D, F
Case 5:
From E/G, exactly one should be selected which is G. Based on condition 1, both C & D are selected. A & F can't be selected together which gives us two possibilities.
9. G, C, D, A
10. G, C, D, F
Therefore, there are 10 possibilities for selecting the team of 4 Students.
Answer: 10
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