Moderate Bar Charts Solved QuestionData Interpretation Discussion

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 $V$.

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: 3/5 For  how  many  siblings,  the  three  sports  chosen  by  them  can  be  uniquely  determined?
 ✖ A. Six ✖ B. Five ✔ C. Four ✖ D. Three ✖ E. Two

Solution:
Option(C) 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, form 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

Except for Atif and Aaqib, for every other sibling the sports chosen by them can be uniquely determined. Hence, the required answer is 4