# Conditions and Grouping Test

CONDITIONS AND GROUPING TEST

For a particular event to occur certain conditions are posed. These conditions are combined to

form certain arrangement or a group. To answer such types of questions, one can make use of

conditional notations for events occurring and group them to answer.

Examples:

Direction: A team is to be selected out of the four boys - Prashant, Amit, Sood and Gupta - and the four girls - Ruchi, Neha, Deepti and Sriya - such that the team should have at least two boys and two girls. Further conditions are as follows:

(i) If Ruchi is selected, neither Amit nor Sood can be selected.

(ii) If Prashant is selected, Gupta is also selected.

(iii) Sriya will be in the team only if Sood is also in the team.

(iv) Amit, if selected would not like to have Neha in the team.

Question: If Ruchi is a part of th team, then who among the following will definitely not be a part of the team ?

- Prashant
- Deepti
- Sriya
- Gupta

Solution : Sriya

If Ruchi is selected, then both Amir and Sood cannot be selected, and Sriya will be in the team only if Sood is also in the team. Therefore, Sriya cannot be a part of the team.

Question : If Sriya and Deepti are part of a team of four, then who will definitely be a part of the team ?

- Prashant
- Deepti
- Sriya
- Cannot be determined

Solution : Cannot be determined

Is Sriya and Deepti are part of a team of four, it means that two boys have to be selected. Since Sriya is selected therefore Sood will be definitely selected. Now , the second boy can be either Amit or Gupta. Therefore, the answer cannot be determined.

Direction: At Pioneer Career Kolkata six students A, B, C, D, E and F aspire to be a member of organizing team of New Year Party The team should have at least two people with following conditions.

(i) If the size of the team is less than 4 then D and F cannot be selected together.

(ii) If B is selected then D should also be selected while E should be rejected.

(iii) If A is selected then exactly one from B and C should also be selected.

(iv) If C is selected then E should also be selected while F should be rejected.

Question : If team size is **3** then which one of the following can not be a part of the team?

- B
- A
- F
- None of these

Solution : F

Lets consider the different cases here

Case (i): Teams with 2 members:

A cannot be a member of any such team as otherwise at least one of B and C must be selected ( From condition (ii) and if B is selected then D also and if C is selected then E also hence in this case number of teams would be more than Possible teams are:

(B, D), (C, E), (D, E ) and (E, F)

Case (ii): Teams with 3 members: Possible teams with 3 members are (A, C, E), (A, B, D), (C, E, D)

Case (iii): Teams with 4 members: Possible teams with 4 members are (A, B, D, F), (A, C, E, D)

Team with 5 or 6 members is not possible.

From the case (ii) we can say that F can not be a part of the team.

Question : What could be the strength of team if **C and E** are always part of the team?

- 2
- 3 or 4
- 2 or 3
- None of these

Solution : None of these

Lets consider the different cases here

Case (i) Teams with 2 members :

A cannot be a member of any such team as otherwise at least one of B and C must be selected ( From condition (ii) and if B is selected then D also and if C is selected then E also hence in this case number of teams would be more than Possible teams are:

(B, D), (C, E), (D, E ) AND (E, F)

Case (ii) Teams with 3 members : Possible teams with 3 members are (A, C, E), (A, B, D), (C, E, D)

Case (iii) Teams with 4 members : Possible teams with 4 members are (A, B, D, F), (A, C, E, D)

Team with 5 or 6 members is not possible.

From all the three available cases **A and C** can be a member of the team that has strength **2 or 3 or 4**