Understanding the Question: Finding the Odd Letter Cluster

The question asks us to identify the letter cluster that is different from the other three based on a certain pattern. We are given four letter clusters: CAX, AYZ, FDZ, and HDS. We need to analyze the relationship between the letters within each cluster to find the one that doesn't follow the rule common to the others.

Analyzing the Given Letter Clusters

Let's look at the alphabetical position of each letter in the given clusters:

Identifying the Pattern

Let's examine the relationship between the letters in each cluster. A common pattern in such questions involves the difference between the alphabetical positions of consecutive letters or the first two letters.

Let's try finding the difference between the alphabetical position of the first letter and the second letter in each cluster:

Applying the Pattern to Each Cluster

• CAX: The position of C is 3 and A is 1. The difference is \(3 - 1 = 2\).
• AYZ: The position of A is 1 and Y is 25. Considering the alphabet wraps around, moving from A backward to Y takes 2 steps (A → Z → Y). The difference can be considered as 2. Or, \(1 - 25 = -24\), and \(-24 + 26 = 2\) (modulo 26).
• FDZ: The position of F is 6 and D is 4. The difference is \(6 - 4 = 2\).
• HDS: The position of H is 8 and D is 4. The difference is \(8 - 4 = 4\).

Based on this analysis, we can see a consistent pattern in the first three clusters: the difference between the alphabetical positions of the first and second letter is 2. However, in the cluster HDS, the difference is 4.

Determining the Odd One Out

Since CAX, AYZ, and FDZ all follow the pattern where the difference between the positions of the first two letters is 2 (considering wrap-around), HDS is the cluster that does not follow this pattern, as its difference is 4.

Therefore, HDS is the odd letter-cluster among the given options.

Revision Table: Letter Positions

Here is a quick reference for the alphabetical positions of letters:

Additional Information: Letter Series Reasoning

Letter series and letter cluster questions are common in logical reasoning sections of various exams. They test your ability to identify patterns in sequences of letters. Common patterns include:

• Difference in alphabetical position between consecutive letters.
• Sum or product of alphabetical positions.
• Vowel/consonant patterns.
• Reverse alphabetical order.
• Skipping letters in a sequence.
• Combining number and letter patterns.

To solve these questions effectively, it's helpful to know the alphabetical position of each letter and practice identifying different types of patterns quickly.