The correct option is B - I and III only.
[as per provisional answerkey]
Step-by-step Trace
We have 7 persons (A, B, C, D, E, F, G) and 3 cars (X, Y, Z). Let's map the distribution based on the given conditions:
- Condition 1: "Only E travels with G." This means E and G are in a car together, and no one else is with them. This pair must occupy one car entirely.
- Condition 2: "A and another two of them travel by X." This means Car X has exactly 3 people: A + two others.
- Condition 3: Since Car X has 3 people and the E-G pair must be alone in a car, E and G cannot be in Car X. Therefore, E and G must be in either Car Y or Car Z.
- Condition 4: "C travels by Z."
- Condition 5: "B does not travel by Y." Also, "A and B do not travel by the same car." Since A is in X, B cannot be in X. If B is not in X and not in Y, B must be in Car Z.
- Condition 6: Now we look at the E-G pair again. They must be in a car alone. Car X has 3 people. Car Z already has C and B. Therefore, E and G must be in Car Y.
- Condition 7: We have accounted for A (Car X), B (Car Z), C (Car Z), E (Car Y), and G (Car Y). The remaining persons are D and F. Since Car X needs "A and another two," D and F must be in Car X.
Final Distribution:
Car X: A, D, F (3 persons)
Car Y: E, G (2 persons)
Car Z: C, B (2 persons)
Evaluating the Statements:
I. No one travels alone: Correct. Car X has 3, Y has 2, and Z has 2.
II. Only D travels with F: Incorrect. D and F travel with A in Car X.
III. Only C travels with B: Correct. Car Z contains only C and B.
Why the other options are incorrect
- Option (a) - I and II only: Statement II is false because D and F are not alone; they are traveling with A in Car X.
- Option (c) - II and III only: Statement II is false as explained above; furthermore, this option omits the fact that Statement I is logically correct.
- Option (d) - All the three: This is incorrect because Statement II contradicts the condition that Car X contains A plus two others (D and F).
Key Concept
Logical deduction through elimination and constraint satisfaction, specifically identifying fixed pairs and distribution limits across multiple groups.