GATE CH 2022 | GA | Question: 4

Question

Six persons $\text{P, Q, R, S, T and U}$ are sitting around a circular table facing the center not necessarily in the same order. Consider the following statements:

• $\text{P}$ sits next to $\text{S}$ and $\text{T}$.
• $\text{Q}$ sits diametrically opposite to $\text{P}$.
• The shortest distance between $\text{S}$ and $\text{R}$ is equal to the shortest distance between $\text{T}$ and $\text{U}$.

Based on the above statements, $\text{Q}$ is a neighbor of

• A. $\text{U}$ and $\text{S}$
• B. $\text{R}$ and $\text{T}$
• C. $\text{R}$ and $\text{U}$
• D. $\text{P}$ and $\text{S}$

Comments

P sits next to S and T.

The statement as given is ambiguous and can be interpreted in two ways:

1. P sits between S and T.
2. P sits next to the pair of both S and T, but not necessarily between them.

In formal logic and puzzle-solving, we typically interpret "sits next to" to mean "is adjacent to" without specifying the exact order. This means P could be between S and T, or P could be on one end with S and T on either side of P.

all the possibilities:

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great analysis @anujs bhai.

Answer 1

Given that, six persons $\text{P, Q, R, S, T}$ and $\text{U}$ are sitting around a circular table facing the center not necessarily in the same order.

• $\text{P}$ sits next to $\text{S}$ and $\text{T}$.
• $\text{Q}$ sits diametrically opposite to $\text{P}$.
• The shortest distance between $\text{S}$ and $\text{R}$ is equal to the shortest distance between $\text{T}$ and $\text{U}$.

Based on the above statements, we can draw the sitting arrangements.

We can also draw the diagram, by changing the position of $\text{S, T}$ and $\text{R, U},$ because there is no restriction for these persons.

Based on the above two diagrams, $\text{Q}$ is a neighbor of $\text{R and U}.$

Correct Answer $:\text{C}$

Comments

why not stp or tsp statement saying p sit next to s and t

Answer 2

 

Let us arrange the 6 seats as positions 1–6.

Since Q is diametrically opposite P, place:

• P = 1
• Q = 4

Since P sits next to S and T, S and T must occupy the two seats adjacent to P:

• S, T = 2 and 6

The remaining seats 3 and 5 are for R and U.

The condition
shortest distance(S,R) = shortest distance(T,U)
forces R and U to occupy 3 and 5 respectively (in either matching arrangement).

So the arrangement is essentially:

P – S – R – Q – U – T

Therefore, the two people sitting next to Q are:

R and U

Answer: C. R and U