UPSC Prelims 2026 CSAT, question 33

Topic: Arrangements and puzzles

Q33

$P,Q,R,S$ and $T$ are ranked 1 to 5 (not necessarily in that order). The rank of $P$ is 4, the rank of $Q$ is not 5, the rank of $R$ is 1, the rank of $S$ is not 2, the rank of $T$ is not 3. Then which of the following is/are correct?

I. If the rank of $S$ is 3, then that of $T$ is 2.

II. If the rank of $Q$ is 3, then that of $T$ is 5.

Select the answer using the code given below.

(a) I only
(b) II only
(c) Both I and II
(d) Neither I nor IICorrect answer

Solution.

Answer: (d) Neither I nor II

Since the rank of $R$ is $1$ and the rank of $P$ is $4$ , the remaining ranks for $Q, S,$ and $T$ are $\{2, 3, 5\}$ subject to $Q \ne 5$ , $S \ne 2$ , and $T \ne 3$ .
Statement I is incorrect: if $S = 3$ , the remaining ranks for $Q$ and $T$ are $\{2, 5\}$ ; since $Q \ne 5$ , we must have $Q = 2$ and $T = 5$ (not $2$ ).
Statement II is incorrect: if $Q = 3$ , the remaining ranks for $S$ and $T$ are $\{2, 5\}$ ; since $S \ne 2$ , we must have $S = 5$ and $T = 2$ (not $5$ ).