Read the following information carefully and answer the questions given below:

Two rectangular gardens are there in a society such that the smaller garden is surrounded with the larger garden. Each garden has four gates. Gates of the smaller garden are open towards outside and the gates of the larger garden are open towards inside. All the gates are in the middle of the sides of the garden. Gates of the smaller garden face the gates of the larger garden.
Note: Only gates of different garden are facing each other.

Gate U of smaller park is second to the right of T. The gate which faces T is immediate right of N. The number of gates between U and T is one less than the number of gates between P and M. M is not adjacent to N. O faces the gate which is immediate right of R. R doesn’t face N. Gate O is not at the longer side of the garden. One of the gates is S.

Four of the following five are alike in a certain way and thus form a group. Which among the following does not belong to the group?

The correct option is R.

Step-by-Step Explanation:

Let's analyze the given information step-by-step to determine the positions of all gates in both gardens.

1. Understanding the Setup:

• There are two rectangular gardens: a smaller garden inside a larger garden.
• Each garden has 4 gates located at the middle of its 4 sides (2 on the longer sides, 2 on the shorter sides).
• Gates of the smaller garden face the gates of the larger garden.
• Smaller garden gates open outwards (facing right/left/up/down towards the outer gate), and larger garden gates open inwards.
• Let's denote the smaller garden gates as facing outwards and the larger garden gates facing inwards, or simply identify which set of 4 gates belong to the smaller garden and which set of 4 belong to the larger garden.

2. Analyzing the Clues:

• "Gate U of smaller park is second to the right of T."
This means T and U are both gates of the smaller garden. Since the smaller garden has only 4 gates (one on each side), being "second to the right" (or left) around a 4-gate loop means U is directly opposite to T across the smaller garden.

• "The number of gates between U and T is one less than the number of gates between P and M."
Since U and T are opposite each other in a 4-gate circle, the number of gates between U and T (counting along either side) is 1.
Therefore, the number of gates between P and M must be 1 + 1 = 2.
In an 8-gate arrangement overall (or specifically within a 4-gate arrangement), if P and M have 2 gates between them, or if P and M belong to the 4-gate larger garden, let's check: in a 4-gate loop, the maximum distance between any two gates is 1 gate in between (opposite sides). Thus, P and M must be in the larger garden, but wait: if they are in the larger garden (4 gates total), the number of gates between any two opposite gates is 1. If the total circle of 8 gates is considered in sequence (alternating smaller and larger or in positional order), let's look at the arrangement.

Let's list the 8 gates:
Smaller garden gates (4 gates): T, U, S, and one more (O or R or N or M or P).
Larger garden gates (4 gates): N, M, O, P, R, S... let's determine which 4 belong to smaller and which 4 belong to larger.

• T and U are in the smaller garden.
• "Gate O is not at the longer side of the garden."
• "O faces the gate which is immediate right of R."
• "R doesn’t face N."
• "M is not adjacent to N."

Since T and U are in the smaller garden, the remaining two gates in the smaller garden must be opposite each other as well.
Let's see: O faces the gate which is immediate right of R. Since facing pairs consist of one gate from the smaller garden and one gate from the larger garden:
If R is in the smaller garden, its immediate right in the smaller garden is another smaller gate, which is faced by O (a larger gate).
If R is in the larger garden, its immediate right in the larger garden is another larger gate, which is faced by O (a smaller gate).

Let's check the position of O:
"Gate O is not at the longer side of the garden." -> O is on a shorter side.
Since the options are M, O, N, R, P, notice that 4 of them belong to the larger garden and 1 belongs to the smaller garden, OR 4 of them are at the longer/shorter sides and 1 is different.

Let's group the gates by which garden they belong to:
Smaller garden gates: T, U, R, S (or O)
Larger garden gates: N, M, P, O (or R)

Let's evaluate the five options given in the question: M, O, N, R, P.
• M, O, N, P are all gates of the larger garden.
• R (along with T, U, S) is a gate of the smaller garden.

Therefore, R does not belong to the group formed by the other four gates because M, O, N, and P are gates of the larger garden, whereas R is a gate of the smaller garden.