**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:**Â What would be the size of the largest possible team?

(a) 8

(b) 7

(c)Â 6

(d) 5

(e) Cannot be determined

**Question 2 :Â **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)Â Only 4

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

(a) 2

(b) 3

(c)Â 4

(d) 5

(e) 6

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

(a) B

(b) C

(c) D

(d) E

(e)Â F

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

(a) *AÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â *

(b) B

(c) C

(d) E

(e)Â G* Â Â Â Â Â Â Â Â Â *

### Answers and Explanations

**Answer 1:Â (d)Â **

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

**Answer 2:Â ****(e)Â **

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.*

**Answer 3:Â (e)**

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.

**Answer 4:Â (a)**

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.

**Answer 5: (c)**

From statement (1): One of *E, G, H *has to be selected to make a team of H. *‘H’ *will be selected (leaving E and *G).*

Now, if ‘H’ is chosen, *‘I’ *has to be chosen (condition 4). If *I *is chosen, *‘B’ *cannot be chosen (condition 5). Further, *‘A’ *cannot be chosen (condition 3). From condition (2) C or F has to be chosen.Â

*Â *

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Hello. In question 2nd, the answer can 2 or 3 or 4 because two members can also for a team(A and B). Similarly 3(ABE) and 4(ABEC). Why is the answer only 4

It is because, one member should be from the groups EGH and CF each. So we have 2 members from these two groups. Now if A and B is also included then the size of the team will be 4. AB and ABE are not possible as they contradict the first two conditions.