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Directions (Qs. 1-5): Answer the questions on the basis of the information given below :
A,B,C,D,E,F,G,H,I and J are the only ten members in a department. There is a proposal to form a team from within the members of the department, subject to the following conditions:
1. A team must include exactly one among E, G and H.
2. A team must include either C or F, but not both.
3. B and D cannot be members of the same team.
4. B and I cannot be members of the same team.
5. If a team includes A, then it must also include B and vice-versa.
6. If a team includes one among H, I and J, then it must also include the other two.
The size of a team is defined as the number of members in the team.

Question 1: What would be the size of the largest possible team?

(a) 8
(b) 7
(c) 6
(d) 5
(e) Cannot be determined

Question 2 : What could be the size of a team that includes A?

(a) 2 or 3
(b) 2 or 4
(c) 3 or 4
(d) Only 2
(e) Only 4

Question 3: In how many ways a team can be constituted so that the team includes D?

(a) 2
(b) 3
(c) 4
(d) 5
(e) 6

Question 4: Who cannot be a member of a team of size 3?

(a) B
(b) C
(c) D
(d) E
(e) F

Question 5: Who can be a member of a team of size 5?

(a) A
(b) B
(c) C
(d) E
(e) G

To from the largest team find, from the compliance of condition (6), we get three members of the team as HIJ. At the same time condition (1) is complied. Following, condition (2) takes either C or F, let us take C and select one more member D because B cannot be chosen as it does not combine with D and I.

Hence, the team members are: HIJCD

If a team which includes A is to be selected, then we cannot take any of HIJ because conditions (3), (5) and (6) are violated. Now let us start with condition (3), then two members of the team are AB. Following condition (1), take one out of EG (I cannot be taken as mentioned earlier). Let us take E. Now, as per condition (2), take one out of CF say C. Then, the size of the team is ABEC.

If a team includes D, it cannot include B and therefore, not even A (from statements 5 and 3). According to condition (1), one out of EGH to be included and as per condition (2), one out of CF is to be selected.

So, following cases are possible:

EFD GFD ECD GCD

If ‘H’ is selected, then we have following groupings :

HIJCD,HIJFD

Hence, the total number of possible cases are 4 + 2 = 6.

We can form a team of size 3 by taking any member out of C, D, E, F. But, B cannot be a part of the team of size 3, because of the following reasons.

From conditions (1) and (2); one of E, G, H and one of C, F are to be selected.

But from statement (3), (A, B) are always together. Hence, B cannot be included in a team of 3 members.