Which one set of letters, when placed sequentially in the blanks of the series x _ z x _ y _ z _ x _ x y y _ z z z, will correctly complete the letter pattern?

Introduction / Context:
This problem belongs to the category of missing letter series. You are given a sequence of x, y, and z with some blanks, and you must choose one option that fills all blanks so that the overall sequence follows a clear and systematic pattern. Such questions train your ability to recognise structured repetition and increasing patterns in symbolic sequences, a key skill in aptitude tests and reasoning examinations.

Given Data / Assumptions:

• Given series: x _ z x _ y _ z _ x _ x y y _ z z z.
• There are six blanks which must be filled sequentially by letters from one chosen option.
• The same underlying pattern should hold from the first letter to the last after filling the blanks.

Concept / Approach:
The letters used are only x, y, and z. A natural idea is to look for a pattern in the counts of each letter. On inspection, we suspect the series builds in groups where the number of x, y, and z increases gradually. A very neat pattern in such questions is to have one x, one y, one z, then two x, two y, two z, and then three x, three y, three z. If we can reconstruct the full sequence to match this idea, we have likely found the correct answer. We then test each option by filling the blanks and checking whether a simple progression appears.

Step-by-Step Solution:
Step 1: Assume the final series should perhaps show increasing runs of x, y, and z. Step 2: Fill the blanks with letters from option B, yxyzxy, in order. Step 3: The completed series becomes: x y z x x y y z z x x x y y y z z z. Step 4: Group the completed sequence as: x, y, z; then x x, y y, z z; then x x x, y y y, z z z. Step 5: Check the counts: each of x, y, and z appears once, then twice, then three times in consecutive blocks, exactly matching an elegant increasing pattern. Step 6: This confirms that option B produces a very regular and purposeful construction, which is typical of well-set reasoning questions.

Verification / Alternative check:
To verify, count the occurrences of each letter. There are 6 x letters, 6 y letters, and 6 z letters. Their arrangement is not random but ordered into segments that show the counts 1, 2, and 3 in sequence. Also, check that there is no sudden disruption where a different letter intrudes into these blocks. All transitions follow the idea of x block, then y block, then z block, for each size. No other option arranges the letters so neatly, which gives strong confirmation that we have the intended solution.

Why Other Options Are Wrong:
Option A (zxyxyz) generates a sequence where the distribution of x, y, and z does not form clean increasing blocks; the runs of each letter are irregular and do not follow a simple rule. Option C (xxyyxz) leads to overlapping segments with uneven counts, so the idea of one, two, and three successive occurrences is lost. Option D (yxyxyz) produces some repeated subpatterns but fails to achieve the beautiful progression in counts that is present with option B. Therefore these options do not supply a consistent structural rule across the whole sequence.

Common Pitfalls:
Learners often attempt to match small local fragments only, for example focusing on the first few letters and ignoring the tail of the series. That approach can mistakenly make an incorrect option appear acceptable. Another frequent error is to ignore the possibility of an increasing count pattern and instead look only at permutations of x, y, and z. Systematic reasoning requires checking the entire string for a uniform rule, such as gradually increasing runs or repeated fixed blocks. Taking time to visualise the full series avoids these mistakes.

Final Answer:
The correct set of letters is option B, yxyzxy.