In the pattern XXXXXXYY, XXXXXYXY, XXXXYXXY, XXXYXXXY, XXYXXXXY, which of the following options correctly continues the trend of where the two Y letters appear?

Introduction / Context:
This question presents a string pattern made of X and Y characters. The given sequence is XXXXXXYY, XXXXXYXY, XXXXYXXY, XXXYXXXY, XXYXXXXY, ?. We must identify how the two Y letters move within an 8 character string and then choose the option that correctly continues this movement. Problems like this test a candidate's ability to track positions of multiple special characters simultaneously and recognise a consistent positional trend.

Given Data / Assumptions:

• Each string has 8 characters.• In every term, there are exactly 2 Y characters and 6 X characters.• The rightmost Y seems to stay in the same position while the left Y moves.• The strings in order are: XXXXXXYY, XXXXXYXY, XXXXYXXY, XXXYXXXY, XXYXXXXY.

Concept / Approach:
The method is to index positions from left to right and mark where each Y appears in each term. By listing these positions, we can look for a pattern for the left Y and for the right Y separately. If the right Y remains fixed while the left Y moves step by step, we can determine the exact next position of the left Y, and from that, reconstruct the full string of X and Y characters for the next term in the sequence.

Step-by-Step Solution:
Step 1: Number positions 1 through 8 from left to right.Step 2: Find the positions of Y in each term:• XXXXXXYY → Y at positions 7 and 8.• XXXXXYXY → Y at positions 6 and 8.• XXXXYXXY → Y at positions 5 and 8.• XXXYXXXY → Y at positions 4 and 8.• XXYXXXXY → Y at positions 3 and 8.Step 3: We observe that the rightmost Y is always at position 8.Step 4: The left Y moves leftward one position at each step: 7, 6, 5, 4, 3.Step 5: Continuing this leftward movement, the next position for the left Y must be 2.Step 6: Hence, in the next term, Y should be located at positions 2 and 8, and all other positions should be filled with X.Step 7: A string with Y at positions 2 and 8 is X Y X X X X X Y, which is written as XYXXXXXY.

Verification / Alternative check:
We can quickly verify by listing all strings including the predicted one: XXXXXXYY (Y at 7,8), XXXXXYXY (6,8), XXXXYXXY (5,8), XXXYXXXY (4,8), XXYXXXXY (3,8) and XYXXXXXY (2,8). The movement of the left Y is perfectly regular, and the right Y remains fixed at position 8 in every term. Among the answer choices, XYXXXXXY is the only string matching this pair of positions exactly, so it must be the correct next term in the series.

Why Other Options Are Wrong:
YXXXXXXY places Y at positions 1 and 8, which would represent an extra step to the left beyond the pattern we have observed. That would be the next term after XYXXXXXY, not the immediate next term. XXXXXXYY and XXXXXYXY are simply earlier terms in the sequence and do not advance the pattern. Thus, they cannot serve as the next item in the series. The correct answer must be a fresh string that continues the progression, not a repetition of an earlier element.

Common Pitfalls:
Some candidates may overlook that there are always two Y letters and focus only on one of them, leading to incorrect conclusions about the pattern. Others may miscount positions or think that both Ys move together, which does not match the actual data. A careful, position by position analysis of each string, with explicit numbering from left to right, avoids these issues and leads directly to XYXXXXXY as the consistent continuation.

Final Answer:
XYXXXXXY