Solving the Letter Series Reasoning Question

The question asks us to find the next letter cluster in the given series: EG, FF, HI, KH, OK, TJ, ?.

To solve this type of letter series problem, we need to identify the pattern followed by the letters in each position within the clusters. We will analyze the first letters of each cluster separately and then the second letters.

Analyzing the First Letters of the Series

Let's look at the first letters of each cluster:

• E (from EG)
• F (from FF)
• H (from HI)
• K (from KH)
• O (from OK)
• T (from TJ)
• ? (the next first letter)

Now let's determine the difference in their positions in the English alphabet:

• E to F: F is 1 position after E ($$F = E + 1$$)
• F to H: H is 2 positions after F ($$H = F + 2$$)
• H to K: K is 3 positions after H ($$K = H + 3$$)
• K to O: O is 4 positions after K ($$O = K + 4$$)
• O to T: T is 5 positions after O ($$T = O + 5$$)

We can see a clear pattern in the increments: +1, +2, +3, +4, +5. Following this pattern, the next increment should be +6.

The last first letter is T. Adding 6 positions to T:

$$T + 6 \text{ positions}$$

T is the 20th letter of the alphabet. The 20th letter + 6 = 26th letter. The 26th letter is Z.

So, the first letter of the next cluster is Z.

Analyzing the Second Letters of the Series

Now let's look at the second letters of each cluster:

• G (from EG)
• F (from FF)
• I (from HI)
• H (from KH)
• K (from OK)
• J (from TJ)
• ? (the next second letter)

Let's determine the difference in their positions in the English alphabet:

• G to F: F is 1 position before G ($$F = G - 1$$)
• F to I: I is 3 positions after F ($$I = F + 3$$)
• I to H: H is 1 position before I ($$H = I - 1$$)
• H to K: K is 3 positions after H ($$K = H + 3$$)
• K to J: J is 1 position before K ($$J = K - 1$$)

We can see a repeating pattern in the increments: -1, +3, -1, +3, -1. Following this pattern, the next increment should be +3.

The last second letter is J. Adding 3 positions to J:

$$J + 3 \text{ positions}$$

J is the 10th letter of the alphabet. The 10th letter + 3 = 13th letter. The 13th letter is M.

So, the second letter of the next cluster is M.

Combining the Patterns

The next first letter is Z, and the next second letter is M. Combining these, the next letter cluster in the series is ZM.

The series continues as EG, FF, HI, KH, OK, TJ, ZM.

Final Answer

Based on the identified patterns for both the first and second letters of the clusters, the letter-cluster that replaces the question mark is ZM.

Revision Table: Letter Series Pattern

Additional Information: Tips for Solving Letter Series

Letter series questions are common in reasoning sections of competitive exams. Here are some tips to help you solve them effectively:

• Write down the Alphabet: Having the alphabet handy with their positions (A=1, B=2, ...) can be very helpful.
• Look for Patterns: Patterns can involve addition or subtraction of letter positions, skipping letters, alternating patterns, or even multiple patterns combined.
• Analyze Each Position Separately: In letter clusters, analyze the first letters, second letters, and so on, independently.
• Consider Alternating Series: Sometimes the pattern applies to alternate terms in the series.
• Check for Reverse Alphabetical Order: The pattern might involve moving backward in the alphabet.
• Practice: Solving more letter series problems will help you recognize different types of patterns quickly.