Ten Students - A,vB, C, D, E, F, G, H, I & J are chosen to represent their college in 4 sports - Tennis, Badminton, Table Tennis & Snooker. The Badminton team has one student less than the Tennis team. A, B and C are not Tennis players individually or as a group. D, E and F are not Badminton players individually or as a group. G, H and I are not Table Tennis players individually or as a group. J is a Table Tennis player. None of the students is a snooker player.

1. Which of the following students could be Table Tennis players - JBG , JCF , JDEF , JBCD ?

2. of those listed, what is the largest possible number of students who could be Table Tennis players - 6 or 7 or 9 or none of these ?

3. if no other student except I is in the Badminton Team, which of the following students could be Tennis players - DH , FE , EG , GH ?

4. if the Table Tennis team has one member, who of the following must be a Tennis player - A , B , D , G ?

5. if G , H and C are the only students in the Badminton Team, which three must be the only students who are Table Tennis players - ABJ , ADJ , BEJ , BFJ ?

6. if A and G are the only Badminton players, how many students must be in the table tennis team - 2 or 3 or 5 or 6 ?

1Q.

JBG cant be together in T.T as G shouldnt be in T.T

options 3 and 4 are wrong becoz, if the T.T group contains 4 people,

we are left with 6 people to divide between T and B groups, and it is given, If T contains some x ppl then, B contains x-1 people (one person less than T)

So, we are left with 6 to give it both x and x-1 

So x+ x-1 = 6

2x-1 = 6, x = 3.5, so the person cant be half :)

So options 3 and 4 are gone, remaining 2 option is the choice.

2Q.

the no. of people in T.T cant be even, as we cant share remaining people between the other groups,

So it has to be 3 or 5 or 7, 9 

9 Cant be possible as 3 people GHI would surely dont go with T.T

So 10-3 = 7,

let us check whether 7 is possible, 

All the people given except, GHI will be T.T and remaining 3 ppl G, H and I would be distributed among T and B, (2 or 1 or vice versa)

3Q.

As G, H and I cant be in T.T, and as B is full with only I

So this 3 ppl (GHI are in the T group for sure)

So GH is the sure option, remaining people A, B, C, D, E and F can go anywhere in either T or in T.T

4Q.

ABC goes to the B (as T.T contains only J)

DEF goes to the T

Question is asking about who is surely T player, D :)

5Q.

So, B consists of GHC and is full

and A, B and C cant be in T group, 

So, AB are in T.T group and J is already in that group, so JAB is for sure.

6Q.

This is very easy question, as B contains 2, T contains 3, and T.T contains = 10 - 3 - 2 = 5 students.

Cheers!!