Nine individuals: Ahmed, Bilal, Danish, Faisal, Haroon, Liaquat...

Each candidate should serve on exactly one of the committees
Every committee must have atleast one member
Committee A should consist of exactly one member more than that of committee B
Among Maryam, Shiza and Zeeshan none can serve on committee A
Among Faisal, Harron and Liaquat none can serve on committee B
Among Ahmed, Bilal and Danish none can serve on committee C

1. In case Danish and Zeeshan are the individuals serving on committee B, how many of the nine individuals should serve on committee C?
A. 2
B. 3
C. 4
D. 5
E. 6

Answer

C. 4

Solution

If Danish and Zeeshan (two persons) are in committee B, then there must be 3 persons in committee A. Hence, 4 persons should serve in committee C.

2. Of the nine individuals, the maximum number that can serve together on committee C is
A. 5
B. 6
C. 7
D. 8
E. 9

Answer

B. 6

Solution

If minimum 1 in committee B, then committee A must have 2 members. Hence, committee C could have maximum of 6 members.

3. In case Ahmed is the only individual serving on committee B, which among the following should serve on committee A?
A. Bilal and Danish
B. Bilal and Faisal
C. Bilal and Liaquat
D. Faisal and Haroon
E. Danish and Haroon

Answer

A. Bilal and Danish

Solution

If Ahmed is the only (one person) serving in committee B. Then committee A must have 2 members. And, committee C cannot have Ahmed, Bilal and Danish. Hence, Bilal and Danish should serve in committee A.

4. In case, any of the nine individuals serves on committee C, which among the following could not be the candidate to serve on committee A?
A. Ahmed
B. Bilal
C. Danish
D. Liaquat
E. Shiza

Answer

E. Shiza

Solution

Committee A cannot have Maryam, Shiza and Zeeshan. Hence, Shiza cannot serve in committee A.

5. In case, Bilal, Danish and Maryam are the only individuals serving on committee B, the total membership of committee C should be
A. 5
B. 4
C. 3
D. 2
E. 1

Answer

D. 2

Solution

If 3 members in committee B then 4 members in committee A. Hence, 2 members in committee C.

6. In case, Bilal, Danish and Maryam are the only individuals serving on committee B, then the members of committee C should be
A. Haroon and Shiza
B. Maryam and Zeeshan
C. Shiza and Zeeshan
D. Faisal and Shiza
E. Haroon and Maryam

Answer

C. Shiza and Zeeshan

Solution

If Bilal, Danish and Maryam (3 persons) are serving in committee B. Then, committee A must have 4 persons and cannot have Maryam, Shiza and Zeeshan. Hence, Shiza and Zeeshan should be in committee C.

7. Among the following combinations which could constitute the membership of committee C?
A. Danish and Shiza
B. Faisal and Maryam
C. Liaquat, Maryam and Shiza
D. Faisal, Haroon and Liaquat
E. Ahmed, Faisal, Maryam and Zeeshan

Answer

B. Faisal and Maryam

Solution

If committee B=1, A=2 then C=6. If committee B=2, A=3 then C=4. If committee B=3, A=4 then C=2. So, committee C cannot have odd number of members. And, committee C cannot have Ahmed, Bilal and Danish. Hence, it should have Faisal and Maryam.

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