Which among the following statement(s) is/are true?

I. E doesn’t sit at the extreme end
II. A has minimum number of bags
III. D sits exactly between B and C

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.

Correct Answer: Both I and III

Step-by-Step Explanation:

1. Understanding the Conditions:

Six persons (A, B, C, D, E, F) sit in a single row facing North.

Number of bags each person has is between 15 and 60 (inclusive: 15 ≤ Bags ≤ 60).

2. Seating Arrangement Derivation:

• Condition: Only two persons sit between E and the person with 35 bags, and neither sits at the extreme ends.

Since six positions exist (let's number them 1 to 6 from left to right) and neither E nor the one with 35 bags is at position 1 or 6, they must occupy positions 2 and 5.

Case 1: E is at position 2, and the person with 35 bags is at position 5.

Case 2: The person with 35 bags is at position 2, and E is at position 5.

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

If E is at position 2: Persons to the right of E = 4. Thus, persons to the left of A = 4 + 1 = 5, which means A sits at position 6 (extreme right).

If E is at position 5: Persons to the right of E = 1. Thus, persons to the left of A = 1 + 1 = 2, which means A sits at position 3.

• Condition: A sits adjacent to C, and the person with (C - 2) bags sits second to the left of A.

Let's evaluate Case 1 (E at 2, A at 6):

If A is at 6, then C must be at 5 (since A and C are adjacent). But position 5 has 35 bags. The person second to the left of A (position 4) has (C - 2) = 35 - 2 = 33 bags.

Now consider F sitting to the immediate right of D (D, F):

Positions 1, 3, 4 are open for remaining persons B, D, F.

D and F must be adjacent in the order D, F. Thus D must be at 3 and F at 4, leaving B at 1.

So the seating order from position 1 to 6 is: B, E, D, F, C, A.

Let's check the positions:

Position 1: B

Position 2: E

Position 3: D

Position 4: F (has C - 2 bags)

Position 5: C (has 35 bags)

Position 6: A

Let's verify statement III: "D sits exactly between B and C"

In the arrangement (B at 1, E at 2, D at 3, F at 4, C at 5), D is at position 3, which is equidistant (2 steps) from B (position 1) and C (position 5). Therefore, D sits exactly between B and C.

Let's verify statement I: "E doesn’t sit at the extreme end"

E is at position 2, which is not an extreme end. So statement I is true.

3. Bag Counts Derivation:

• C has 35 bags.

• F has C - 2 = 35 - 2 = 33 bags.

• D has an even square number of bags. Between 15 and 60, the even squares are 16 ($$₄²) and 36 ($$₆²).

• B has 20 bags more than D: If D = 16, B = 36. If D = 36, B = 56.

• A has 18 bags less than B: If B = 36, A = 18. If B = 56, A = 38.

• E has 15 bags more than the one two places away from B. Two places away from B (position 1) is D (position 3). So E = D + 15.

If D = 16, then E = 16 + 15 = 31 (which is a prime number, matching the condition that E has a prime number of bags).

Thus: D = 16, B = 36, A = 18, E = 31, C = 35, F = 33.

Here, D has 16 bags, which is the minimum number of bags (less than A's 18 bags). Therefore, statement II ("A has minimum number of bags") is false.

Conclusion:

Statements I and III are true.