Question

Read the following information carefully and answer the questions that follow.
(i) There are six students ( $A$ , $B$ , $C$ , $D$ , $E$ and $F$ ) in a group. Each student can opt for only three choices out of the six which are music, reading, painting, badminton, cricket and tennis.
(ii) $A$ , $C$ and $F$ like reading.
(iii) $D$ does not like badminton, but likes music.
(iv) Both $B$ and $E$ like painting and music.
(v) $A$ and $D$ do not like painting, but they like cricket.
(vi) All students except one like badminton.
(vii) Two students like tennis.
(viii) $F$ does not like cricket, music and tennis.
How many students like painting and badminton?
(A) $1$
(B) $2$
(C) $3$
(D) $4$

Answer 1

Hint: Here in this question we have been given information in the form of some statements. We will simplify them and make a list of students and their hobbies to answer the question.

Complete step by step answer:
Now considering the question we have 8 statements.
Hence we can say that
Reading is opted by $A$ , $C$ and $F$ .
Music is opted by $D$ , $B$ and $E$ .
Painting is opted by $E$ and $B$ .
Painting is not opted by $A$ and $D$ .
Cricket is opted by $A$ and $D$ .
Badminton is not opted for by $D$ .
Badminton is opted by $A$ , $B$ , $C$ , $E$ and $F$ .
Tennis is opted by two students.
$F$ has not opted for music and cricket.
Now as we can see that $A$ , $B$ and $E$ has already opted for three choices. Remaining is $C$ , $D$ and $F$ . Tennis is opted by $C$ and $D$ only. We can note that $F$ has only two options: Reading, Badminton and one option is pending which is painting.
From the given information we can give the list of students and their hobbies as follows:
$A$ likes reading, badminton and cricket.
$B$ likes music, painting and badminton.
$C$ likes reading, tennis and badminton.
$D$ likes music, cricket and tennis.
$E$ likes music, painting and badminton.
$F$ likes reading, badminton and painting.

Therefore we can conclude that $B$, $E$ and $F$ like badminton and painting.

So, the correct answer is “Option C”.

Note: While answering questions of this type we should be sure with the conclusions that we derive from the given statements. If we derive any wrong conclusion then our answer would be wrong.