UPSC Prelims 2026 CSAT, question 35

Topic: Arrangements and puzzles

Q35

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.

(a) I and II only
(b) I and III onlyCorrect answer
(c) II and III only
(d) All the three

Solution.

Answer: (b) I and III only

Car $X$ carries $A$ and two others (3 persons); since only $E$ travels with $G$ , $\{E, G\}$ occupy a car of size 2 alone, and since $C$ is in $Z$ , we have $Y = \{E, G\}$ .
Because $B$ is neither in $Y$ nor in the same car as $A$ (car $X$ ), $B$ must travel in $Z$ with $C$ , leaving $D$ and $F$ to join $A$ in $X$ ; thus $X = \{A, D, F\}$ , $Y = \{E, G\}$ , and $Z = \{B, C\}$ .
Statements I and III are correct (no one travels alone, and only $C$ travels with $B$ in car $Z$ ), whereas Statement II is incorrect because $A$ also travels with $D$ and $F$ in car $X$ .