A, B, C, D, E, F and G are travelling in three different vehicles: Swift, Creta, and Nexon. There are at least two passengers in each vehicle. Among them, only two are male. There are two engineers, two doctors and three teachers. (i) C is a lady doctor and she does not travel with A and F, who are sisters. (ii) B, a male engineer, travels with only G, a teacher, in a Swift. (iii) D is a male doctor. (iv) Two persons belonging to the same profession do not travel in the same vehicle. (v) A is not an engineer and travels in a Creta. (vi) The pair of sisters A and F travels in the same vehicle. What is the profession of F?
Step-by-step Solution:
From the condition, Swift must contain $B(E)$ and $G(T)$. Since $C$ and $D$ are both doctors, they cannot travel together. $A$ and $F$ are sisters and must travel in the same vehicle, and since $A$ is in Creta, $F$ must also be in Creta. $D$ cannot travel with $C$, so $D$ also goes to Creta. Thus, Creta contains $A$, $F$, and $D$. In Creta, all three must have different professions. We already know $D$ is a doctor. Therefore, $A$ must be a teacher, which forces $F$ to be an engineer. The remaining persons are $C(D)$ and $E(T)$, who must travel in Nexon. \[ F \text{ is an Engineer.} \]