NIMCET 2016 Logical Reasoning Question 61 with Solution

Question 61

Logical Reasoning Puzzles Easy

A team must be selected from the ten portable players A, B, C, D, E, F, G, H, I and J. Of these, A, C, E and J are forwards, B, G and H are point guards and D, F and I are defenders. The team must have at least one forward, one point guard and one defender. If the team includes J, it must also include F. The team must include E or B, but not both. If the includes G, it must also include F. The team must include exactly one among C, G and I. C and F cannot be members of the same team. D and H cannot be members of the same team. The team must include both A and D or neither of them. There is no restriction on the number of members in the team. What would be size of the largest possible team?

(A) 7

(B) 6

(C) 5

(D) 4

View Dynamic Solution & Explanation ▼

Correct Solution: Option B

Step-by-step Solution:

Quick Solution

To find the largest possible team, we should analyze the most restrictive rule, which is Rule 5: "The team must include exactly one among C, G and I." This splits the problem into three distinct and mutually exclusive cases. We will find the maximum team size possible in each case and then compare them.

Case 1: C is selected for the team

If C is IN, then G and I are OUT.
Rule 6 ("C and F cannot be members") is triggered → F is OUT.
Rule 2 ("If J is in, F must be in") is triggered → Since F is out, J must be OUT.
To maximize the team, we can try to add the remaining players: A, D, B, E, H. We can add A and D (Rule 8), and one of E or B (Rule 3). This gives a team like {C, A, D, B}.
However, checking the composition (1 Forward, 1 Guard, 1 Defender), this team is invalid as it lacks a Point Guard (H is forced out by D). The largest valid team in this case is smaller.
Maximum size in this case is 4.

Case 2: G is selected for the team

If G is IN, then C and I are OUT.
Rule 4 ("If G is in, F must be in") is triggered → F is also IN.
To maximize, we make the following choices:
- Add both A and D (Rule 8).
- This forces H to be OUT (Rule 7).
- Add one from {E, B}. Let's add E (Rule 3).
- We can add J, because F is already in the team (Rule 2).
This gives the team: {G, F, A, D, E, J}. This team is valid and satisfies all rules, including composition.
Maximum size in this case is 6.

Case 3: I is selected for the team

If I is IN, then C and G are OUT.
Similar to the case above, we can build a maximal team by choosing to add A and D, one from {B,E}, and the pair J and F.
This can give a valid team like: {I, A, D, B, F, J}.
Maximum size in this case is 6.

Conclusion

Comparing the maximum possible team size from the three cases (4, 6, and 6), the overall largest possible team has 6 members.

Final Answer: The size of the largest possible team is 6.