Four of the following five are alike in a certain way and thus form a group. Find the one who doesn’t belong to the group?

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

Six persons – A, B, C, D, E and F sit in a row and all are facing north but not in same order as given. Each of them has different number of bags. None of them has bags less than 15 and more than 60. Only two persons sit between E and the one who has 35 bags, and neither of them sits at the extreme ends. The number of persons sitting to the right of E is one less than the number of persons sitting to the left of A. The one who has two bags less than C sits second to the left of A who sits adjacent to C. F sits to the immediate right of D who has even square number of bags. A has 18 bags less than B who has 20 bags more than D. E has prime number of bags and 15 bags more than the one who sits two places away from B.

Identify which of the following statements about the arrangement is/are correct.

I. The person sitting at the 4th position from the left holds more bags than E.
II. A holds the greatest number of bags among all six persons.
III. B occupies one of the two extreme ends of the row.

The correct option is Both I and III.

Let us analyze the given information step-by-step to find the seating arrangement and the number of bags held by each person from left to right (positions 1 to 6).

Step 1: Determine the positions of E, A, C, and the person with 35 bags.

There are 6 positions from left to right, numbered 1 to 6.

1. Only two persons sit between E and the person who has 35 bags, and neither sits at the extreme ends (positions 1 and 6). Therefore, E and the 35-bag holder must occupy positions 2 and 5.

2. The number of persons sitting to the right of E is one less than the number of persons sitting to the left of A:

$\text{Persons to the right of E}=\text{Persons to the left of A}-1$

If E is at position 2, there are 4 persons to the right of E. Thus, there must be $4+1=5$ persons to the left of A, placing A at position 6 (extreme right).

3. A sits adjacent to C, so C must be at position 5. This means C is the person who has 35 bags.

4. The person sitting second to the left of A (position 4) has 2 bags less than C. Thus, the person at position 4 has:

$35-2=33\text{bags}$

Step 2: Determine the positions of D, F, and B.

1. F sits to the immediate right of D. Since positions 2, 5, and 6 are occupied by E, C, and A respectively, the only available consecutive positions for D and F are positions 3 and 4. Therefore, D is at position 3 and F is at position 4 (holding 33 bags).

2. The remaining position 1 is occupied by B.

The seating order from left to right is:

Position 1: B
Position 2: E
Position 3: D
Position 4: F (33 bags)
Position 5: C (35 bags)
Position 6: A

Step 3: Calculate the number of bags held by each person.

1. D has an even square number of bags between 15 and 60. The possible even squares in this range are 16 ($4^2$) and 36 ($6^2$).

2. B has 20 bags more than D: $\text{B}=\text{D}+20$

3. A has 18 bags less than B: $\text{A}=\text{B}-18=\text{D}+2$

4. The person two places away from B (position 1) is D (position 3). E has 15 bags more than D: $\text{E}=\text{D}+15$

5. We are given that E has a prime number of bags:

If $\text{D}=36$, then $\text{E}=36+15=51$ (not a prime number).

If $\text{D}=16$, then $\text{E}=16+15=31$ (which is a prime number).

Therefore, $\text{D}=16$ bags. From this, we find:

B = 16 + 20 = 36 bags
A = 36 - 18 = 18 bags
E = 31 bags
F = 33 bags
C = 35 bags

Final Arrangement & Bag Counts:

Position 1: B (36 bags)
Position 2: E (31 bags)
Position 3: D (16 bags)
Position 4: F (33 bags)
Position 5: C (35 bags)
Position 6: A (18 bags)

Step 4: Evaluate the given statements.

Statement I: The person sitting at the 4th position from the left (F, with 33 bags) holds more bags than E (31 bags). Since $33>31$, Statement I is correct.

Statement II: A holds the greatest number of bags among all six persons. This is incorrect because B has 36 bags, which is greater than A's 18 bags. Statement II is incorrect.

Statement III: B occupies one of the two extreme ends of the row. B is at position 1 (the extreme left end). Statement III is correct.

Thus, statements I and III are correct.