Seven persons A, B, C, D, E, F and G travel by three cars X, Y, Z. A and another two of them travel by X. Only E travels with G. C travels by Z, but B does not travel by Y. Besides, A and B do not travel by the same car. Then which of the following are correct? I. No one travels alone. II. Only D travels with F. III. Only C travels with B. Select the answer using the code given below.

To determine the correct statements, we must systematically analyze the constraints given in this logical reasoning puzzle. There are 7 persons (A, B, C, D, E, F, G) distributed among 3 cars (X, Y, Z).

Step-by-step Deduction:

1. Car X: "A and another two of them travel by X." Thus, Car X contains exactly 3 people: A and two others.
2. Car Y & G's constraint: "Only E travels with G." This implies E and G travel together and are the only occupants of their car (exactly 2 people). Since Car X holds 3 people, E and G cannot be in Car X.
3. Placing B: "C travels by Z." We are told "B does not travel by Y" and "A and B do not travel by the same car" (meaning B is not in Car X). Therefore, B must be in Car Z with C.
4. Finalizing the Cars: With C and B in Car Z, E and G cannot be in Car Z. Thus, E and G must exclusively occupy Car Y. So, Car Y = {E, G} and Car Z = {C, B}.
5. Remaining Persons: The unplaced persons are D and F. Since Car X requires two more people, D and F must join A. Car X = {A, D, F}.

Evaluating the Statements & Options:

• Statement I: True. The cars contain 3, 2, and 2 people respectively; no one travels alone.
• Statement II: False. F travels with both D and A, not only D.
• Statement III: True. B is in Car Z, and its only other occupant is C.

Since Statement II is demonstrably false, Options A, C, and D are all incorrect because they incorrectly validate Statement II. Option B (I and III only) is the only correct choice.

Takeaway: In analytical arrangement puzzles, systematically isolate negative constraints (e.g., determining where B cannot go) to deduce definitive group placements.