Question

If the first and fifth position of the numbers 5, 3, 2, 6, 4, 1, 8, 9 are exchanged and the positions of the second and sixth numbers are also exchanged and so on. Find the sixth number from the right of the rearranged pattern-

• A. 2
• B. 4
• C. 6
• D. 8

Hint:

Notice that "6th from right" in an 8-element list is equivalent to the "3rd from left" (since \( 8 - 6 + 1 = 3 \)). The 3rd position in the new list is occupied by the element swapped from the 7th position of the original list. The 7th element of the original list is 8, so the answer is 8. This saves you from writing out the entire rearranged sequence!

Answer 1

The Correct Option is D

Step 1: Number the original list.
Positions 1 to 8 hold $5,3,2,6,4,1,8,9$.
Step 2: Read the swap rule.
Position 1 swaps with 5, position 2 with 6, position 3 with 7, position 4 with 8.
Step 3: Do the first two swaps.
$5\leftrightarrow4$ and $3\leftrightarrow1$ make seats 1,2,5,6 read $4,1,\dots,5,3$.
Step 4: Do the last two swaps.
$2\leftrightarrow8$ and $6\leftrightarrow9$ fill the rest.
Step 5: Write the new line.
The rearranged order is $4,1,8,9,5,3,2,6$.
Step 6: Count six from the right.
From the right: $6,2,3,5,9,8$, so the sixth is $8$.
\[ \boxed{8} \]