F and J cannot be placed in Group 3 because doing so would force H to be placed in Group 2. This would violate Rule #5, which states that H cannot be placed in Group 2.
Here is how I worked through this problem in more detail:
The question states that G is the only child in Group 1, which means that the other two spots in Group 1 must be filled by adults. We know from the setup that each group consists of exactly three canoeists, and we know from the first rule that there must be at least one adult in each group. We have a total of five children and four adults. From this, we have already established that two adults and one child will be in Group 1. This leaves one adult and two children for Group 2 and one adult and two children for Group 3. This gives us:
1: __ __ G A A C 2: __ __ __ A C C 3: __ __ __ A C C
We know from Rule #3 that G cannot be in the same group as T, which means that T cannot be in Group 1. We know from Rule #5 that T cannot be in Group 2. This means that T must be assigned to Group 3. This gives us: 1: __ __ G A A C 2: __ __ __ A C C 3: T __ __ A C C
We know from Rule #5 that H cannot be in Group 2. Since H is a child, we also know that it cannot be in Group 1 because there are no children spots left. This means that H must be assigned to Group 3. This gives us: 1: __ __ G A A C 2: __ __ __ A C C 3: T __ H A C C
We know from Rule #2 that F and J must be in the same group. Since they are both children, they need to be assigned to a group with two open children spots. Group 1 has no open children spots, Group 2 has two open children spots, and Group 3 has one open children spot. Therefore, F and J must be placed in Group 2. This gives us: 1: __ __ G A A C 2: __ F J A C C 3: T __ H A C C
We only have one child left - K, and one open children spot- in Group 3. Therefore, we assign K to Group 3. This gives us: 1: __ __ G A A C 2: __ F J A C C 3: T K H A C C
These are all the deductions we can make. Because Q, R, and S can be in any of the three remaining open spots, we can eliminate (C), (D), and (E) as choices that do not have to be true. We can eliminate (A) because, as our diagram shows, F is placed in Group 2 and not in Group 3. We can correctly select (B), as our diagram places K in Group 3.
Does that make sense? Please let us know if you have any other questions and best of luck with your studies!
