Question

Seven people, A, B, C, D, E, F and G, want to go boating. Only two boats are available, and their seating must follow these rules:
(I) A will go in the same boat as E.
(II) F cannot go in the same boat as C, unless D also joins them.
(III) Neither B nor C can be placed in the same boat as G.
(IV) A single boat can carry a maximum of four people.

If E is in the same boat as F, which of the following is the complete and accurate list of people in the other boat?

• A. F and E
• B. G and A
• C. D and A
• D. C, D and B

Hint:

Work out who can safely become the fourth passenger with A, E and F without breaking the G avoidance rule or the F-C-D rule.

Answer 1

The Correct Option is D

Check the fourth member of the A, E, F boat by testing each remaining person, B, C, D and G, one at a time against the rules.

1. F and E: These two already sit together in the boat we are examining, so this cannot describe who is left in the other boat.
2. G and A: A is already fixed with E and F in the same boat as G here, so A cannot also appear in the other boat with just G. This pairing is impossible.
3. D and A: A stays with E throughout, by rule I, so A cannot be part of the other boat while E and F occupy the first one.
4. C, D and B: Adding C to the A, E, F boat would need D too by rule II, giving five seats, more than rule IV allows. Adding B or D alone leaves the other three trapped with G, breaking rule III since B and C cannot sit with G. The only clash free setup is G joining A, E and F, leaving B, C and D together in the second boat.

Every other pairing breaks a rule once tested, so B, C and D form the complete list for the other boat.

Let's summarize:

• A, E and F always travel together once E picks F.
• C cannot join without dragging D along, which overfills the boat.
• G is the only person who can safely become the fourth member with A, E, F, leaving B, C, D as the other boat.

So the correct list is C, D and B.

\[ \boxed{\text{C, D and B}} \]