QUESTION

CSAT

Hard

Reasoning

Prelims 2026

Eight persons $P$ , $Q$ , $R$ , $S$ , $T$ , $U$ , $V$ and $W$ sit around a round table in eight different seats placed with equal distance between any two consecutive seats. Both $P$ and $R$ are adjacent to $Q$ . Both $T$ and $R$ are adjacent to $S$ . Both $U$ and $W$ are adjacent to $V$ . $S$ and $W$ are on opposite chairs. If while going in the clockwise direction around the table from $P$ , one meets $R$ before $T$ , then how many persons shall $Q$ cross while moving in the clockwise direction around the table before meeting $W$ ?

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Explanation

Let's break down the given conditions step by step to determine the seating arrangement of the 8 persons around the circular table.

Both $P$ and $R$ are adjacent to $Q$ : This means $Q$ is sitting exactly between $P$ and $R$ . The sequence is either $P-Q-R$ or $R-Q-P$ .
Both $T$ and $R$ are adjacent to $S$ : This means $S$ is sitting exactly between $T$ and $R$ . The sequence is either $T-S-R$ or $R-S-T$ .

Combining the first two conditions, since $R$ is common to both, the 5 persons must sit together in a contiguous block. The sequence of these 5 persons is either $P-Q-R-S-T$ or $T-S-R-Q-P$ .

Both $U$ and $W$ are adjacent to $V$ : This means $V$ is sitting exactly between $U$ and $W$ . The sequence is $U-V-W$ or $W-V-U$ . This forms a block of 3 persons.

Since there are 8 seats in total, these two blocks (one of 5 persons and one of 3 persons) will complete the circle.

$S$ and $W$ are on opposite chairs: In a circular arrangement of 8 seats, opposite chairs have exactly 3 seats between them on either side. Let's assign position numbers 1 to 8 in a clockwise direction. If we place the block $P-Q-R-S-T$ at positions 1 to 5 respectively, $S$ is at position 4. For $W$ to be opposite to $S$ , $W$ must be at position 8 (since $8 - 4 = 4$ ). This leaves positions 6 and 7 for $U$ and $V$ . Since $V$ must be between $U$ and $W$ , $V$ takes position 7 and $U$ takes position 6.

Let's verify the clockwise condition:

"While going in the clockwise direction around the table from $P$ , one meets $R$ before $T$ ". In our arrangement (1: $P$ , 2: $Q$ , 3: $R$ , 4: $S$ , 5: $T$ , 6: $U$ , 7: $V$ , 8: $W$ ), moving clockwise from $P$ (1), we meet $R$ (3) before $T$ (5). This perfectly satisfies the condition! (Note: If the arrangement was placed counter-clockwise, we would meet $T$ before $R$ , which would violate the rule).

Finding the final answer: The question asks: "How many persons shall $Q$ cross while moving in the clockwise direction around the table before meeting $W$ ?"

$Q$ is at position 2.
$W$ is at position 8.
Moving clockwise from $Q$ (2) to $W$ (8), $Q$ will pass by the persons sitting at positions 3, 4, 5, 6, and 7.
These positions are occupied by $R, S, T, U,$ and $V$ .