Analysing Letter Clusters to Find the Odd One Out

The question asks us to identify the letter cluster that is different from the other three based on a certain pattern or rule. To solve such questions, we usually look at the position of the letters in the English alphabet and find relationships between them.

Understanding Alphabet Positions

Let's first assign numerical values to each letter based on its position in the English alphabet (A=1, B=2, ..., Z=26):

Analysing Each Letter Cluster

Now, let's examine each given letter cluster and look for patterns:

1. JPKM

• J is the \(10\text{th}\) letter.
• P is the \(16\text{th}\) letter.
• K is the \(11\text{th}\) letter.
• M is the \(13\text{th}\) letter.

Let's check relationships. What about the first two letters, J and P? Their positions are \(10\) and \(16\). \(10 + 16 = 26\). This is not \(27\).

Letters whose positions sum up to \(27\) are called 'opposite' letters (e.g., A and Z, B and Y). J's opposite is Q (\(10+17=27\)), and P's opposite is K (\(16+11=27\)). So, the first two letters J and P are not opposite letters.

2. KPLN

• K is the \(11\text{th}\) letter.
• P is the \(16\text{th}\) letter.
• L is the \(12\text{th}\) letter.
• N is the \(14\text{th}\) letter.

Let's look at the first two letters, K and P. Their positions are \(11\) and \(16\). \(11 + 16 = 27\). K and P are opposite letters.

3. DWEG

• D is the \(4\text{th}\) letter.
• W is the \(23\text{rd}\) letter.
• E is the \(5\text{th}\) letter.
• G is the \(7\text{th}\) letter.

Let's look at the first two letters, D and W. Their positions are \(4\) and \(23\). \(4 + 23 = 27\). D and W are opposite letters.

4. FUGI

• F is the \(6\text{th}\) letter.
• U is the \(21\text{st}\) letter.
• G is the \(7\text{th}\) letter.
• I is the \(9\text{th}\) letter.

Let's look at the first two letters, F and U. Their positions are \(6\) and \(21\). \(6 + 21 = 27\). F and U are opposite letters.

Identifying the Odd One Out

Based on our analysis:

• In KPLN, the first two letters (K and P) are opposite letters.
• In DWEG, the first two letters (D and W) are opposite letters.
• In FUGI, the first two letters (F and U) are opposite letters.
• In JPKM, the first two letters (J and P) are NOT opposite letters (\(10+16=26\)).

The pattern that holds true for three of the letter clusters (KPLN, DWEG, FUGI) is that the first two letters are a pair of opposite letters. The cluster JPKM does not follow this pattern.

Therefore, JPKM is the odd one out.

Understanding Opposite Letters

Opposite letters are pairs of letters that are equidistant from the beginning and end of the alphabet. Their positions sum to 27. Here is a list of opposite letter pairs:

Using this table confirms that K&P, D&W, and F&U are opposite pairs, but J&P are not.

Conclusion: Identifying the Odd Letter Cluster

The letter cluster JPKM is the odd one out because the relationship between the first two letters (J and P) is different from the relationship between the first two letters in the other three clusters (KPLN, DWEG, FUGI). In KPLN, DWEG, and FUGI, the first two letters are opposite letters, whereas in JPKM, they are not.

Revision Table: Checking Patterns

The revision table clearly shows that JPKM is the only cluster where the first two letters are not an opposite pair.

Additional Information on Letter Series and Reasoning

Letter series and letter cluster questions are common in reasoning sections of competitive exams. They test your ability to identify logical rules and patterns based on the alphabetical order or other characteristics of letters.

Common patterns include:

• Difference or sum of letter positions.
• Alphabetical order (e.g., consecutive letters).
• Vowel/consonant patterns.
• Symmetrical patterns within the cluster.
• Opposite letter pairs.
• Skipping a fixed number of letters.

Practicing different types of letter pattern questions helps you quickly spot the underlying rule and solve the problem efficiently.