Analyzing the Sequence and Interchange Rule

The problem provides a sequence of characters and describes a specific interchange operation involving the first 10 and last 10 terms. We need to determine the fifth term from the right in the new arrangement after this interchange.

The given sequence is: RB75E%M3W48Q9#B2A$MS

Let's first analyze the structure and length of the original sequence.

• By counting, we find the sequence has a total of 20 characters.
• The first 10 terms are: R, B, 7, 5, E, %, M, 3, W, 4.
• The last 10 terms are: 8, Q, 9, #, B, 2, A, $, M, S.

Understanding the Interchange Operation

The rule states that the first 10 terms and the last 10 terms are interchanged. The method of interchange is described as: the first term with the last, the second with the second last, the third with the third last, and so on. This indicates a pairwise swapping of elements based on their positions from the beginning and the end of the entire sequence.

Let the original sequence be denoted by $s_1, s_2, \dots, s_{20}$. The interchange rule means:

• $s_1$ is swapped with $s_{20}$.
• $s_2$ is swapped with $s_{19}$.
• $s_3$ is swapped with $s_{18}$.
• ... and so on, until ...
• $s_{10}$ is swapped with $s_{11}$.

So, the new sequence, $s'_1, s'_2, \dots, s'_{20}$, will have:

• $s'_1 = s_{20}$
• $s'_2 = s_{19}$
• ...
• $s'_{10} = s_{11}$
• $s'_{11} = s_{10}$
• $s'_{12} = s_9$
• ...
• $s'_{20} = s_1$

Forming the New Arrangement

Let's list the original sequence with positions and then show the result of the interchange.

The new arrangement of the sequence is: S M $ A 2 B # 9 Q 8 4 W 3 M % E 5 7 B R

Finding the Fifth Term from the Right

We need to find the fifth term when counting from the right end of the new arrangement. The new sequence has 20 terms.

• The 1st term from the right is the term at position 20.
• The 2nd term from the right is the term at position 19.
• The 3rd term from the right is the term at position 18.
• The 4th term from the right is the term at position 17.
• The 5th term from the right is the term at position 16.

Looking at our table or the new sequence: S M $ A 2 B # 9 Q 8 4 W 3 M % E 5 7 B R

The term at position 16 is E.

Conclusion

After interchanging the terms according to the rule, the fifth term from the right in the new arrangement is E.

Revision Table - Sequence Interchange

Additional Information - Sequence Manipulation Basics

Sequence manipulation questions are common in logical reasoning tests. They involve changing the order or properties of elements in a list based on specific rules. Key skills needed include:

• Careful Observation: Accurately noting the original sequence and its length.
• Understanding Rules: Precisely interpreting the given rule for transformation, whether it's swapping, reversing, deleting, inserting, or applying conditions.
• Step-by-Step Application: Applying the rule methodically to each relevant element or section of the sequence.
• Tracking Positions: Keeping track of the new positions of elements after the manipulation. Using indexing (from left or right) is crucial. Remember that the $n$-th term from the right of a sequence with $L$ elements is the $(L-n+1)$-th term from the left.
• Final Check: Rereading the question to ensure the final answer addresses exactly what was asked (e.g., term at a specific position from left or right, or a count of certain elements).

This problem involved a full sequence reversal via pairwise swaps around the center point between positions 10 and 11.