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: Understanding the Question:
We are given a sequence of numbers and a rule for swapping their positions. We need to find the rearranged sequence and locate the sixth number when counting from the right.

Step 2: Detailed Explanation:
Let the original positions of the numbers be:
- Position 1: 5
- Position 2: 3
- Position 3: 2
- Position 4: 6
- Position 5: 4
- Position 6: 1
- Position 7: 8
- Position 8: 9
Now, let us apply the exchange rules "first and fifth exchanged, second and sixth exchanged, and so on":
- Exchange Position 1 and Position 5: (5 \(\leftrightarrow\) 4)
- Exchange Position 2 and Position 6: (3 \(\leftrightarrow\) 1)
- Exchange Position 3 and Position 7: (2 \(\leftrightarrow\) 8)
- Exchange Position 4 and Position 8: (6 \(\leftrightarrow\) 9)
Now, let's write down the numbers in their new positions (from Position 1 to 8):
- Position 1: 4
- Position 2: 1
- Position 3: 8
- Position 4: 9
- Position 5: 5
- Position 6: 3
- Position 7: 2
- Position 8: 6
The rearranged sequence is: `4, 1, 8, 9, 5, 3, 2, 6`.
We need to find the sixth number from the right of this rearranged pattern:
- 1st from right: 6
- 2nd from right: 2
- 3rd from right: 3
- 4th from right: 5
- 5th from right: 9
- 6th from right: 8
Therefore, the sixth number from the right is 8.

Step 3: Final Answer:
(D) 8