Common Information
Answer the questions on the basis of the information given below.
Each of the six siblings namely Azhar, Atif, Aslam, Aaqib, Armaan and Ahmad are asked to choose three sports out of six different sports namely Cricket, Football, Hockey, Basketball, Swimming and Volleyball. Each of the given sports is chosen by at least one of the siblings. The number of siblings who chose Cricket, Football, Hockey, Basketball, Swimming and Volleyball are denoted by $C, F, H, B, S$ and $V$ respectively. The following bar – graph provides details about the values of $C, F, H, B$ and $V$.
Additional Information Given
I. Atif has chosen exactly one sport, which Armaan did not choose.
II. There are exactly two sports that have been chosen by Azhar as well as Aslam and there are exactly three sports that have not been chosen by Aslam as well as Ahmad.
III. Ahmad chose Cricket and Swimming and Armaan did not choose Basketball.
Q. 
Common Information Question: 1/5 What is the value of $(6 – S)$? 
✔ A.  4 
✖ B.  3 
✖ C.  1 
✖ D.  Cannot be uniquely determined 
Solution:
Option(A) is correct
It is clear that $C + F + H + B + S + V = 18$
Also, from the bar – graph, the value of $C, F, B, H$ and $V$ is $3, 2, 5, 2$ and $4$ respectively.
Therefore,
$S = 18 – (3 + 2 + 5 + 2 + 4) = 2$
Since, the number of siblings who chose Basketball is 5 and there are exactly three sports that have not been chosen by Aslam as well as Ahmad (Additional information II), therefore, Aslam as well as Ahmad chose Basketball.
Also, from additional information II, Aslam and Azhar chose Cricket and Swimming.
Since, the number of siblings who chose Volleyball is $4$, therefore except for Ahmad and Azhar, every other sibling chose Volleyball. Since, Armaan did not choose Basketball and there is one sport that has not been chosen by Armaan but is chosen by Atif, therefore that sport is Basketball.
Also, the three sports chosen by Armaan are Football, Hockey and Volleyball.
Table below can be scrolled horizontally
Azhar 
Atif 
Aslam 
Aaqib 
Armaan 
Ahmad 

Cricket 
Yes 
No 
Yes 
No 
No 
Yes 
Football 
No 
No 
Yes 
No 

Hockey 
No 
No 
Yes 
No 

Basketball 
Yes 
Yes 
Yes 
Yes 
No 
Yes 
Swimming 
No 
No 
Yes 
No 
No 
Yes 
Volleyball 
Yes 
Yes 
No 
Yes 
Yes 
No 
The value of $6  S$
$= 6  2$
$=4$