Finding the Different Letter Cluster

The problem asks us to identify the letter cluster that follows a different pattern compared to the other three. To solve this type of question, we usually look at the positional values of the letters in the English alphabet and find the differences between consecutive letters within each cluster.

Let's assign a numerical value to each letter of the alphabet, where A=1, B=2, and so on, up to Z=26. We will then examine the difference in positional values between adjacent letters in each cluster.

Analyzing Each Letter Cluster

1. BFJNR

• B is the 2nd letter.
• F is the 6th letter. Difference: $6 - 2 = 4$.
• J is the 10th letter. Difference: $10 - 6 = 4$.
• N is the 14th letter. Difference: $14 - 10 = 4$.
• R is the 18th letter. Difference: $18 - 14 = 4$.

The differences between consecutive letters in BFJNR are consistently +4.

2. KOSWA

• K is the 11th letter.
• O is the 15th letter. Difference: $15 - 11 = 4$.
• S is the 19th letter. Difference: $19 - 15 = 4$.
• W is the 23rd letter. Difference: $23 - 19 = 4$.
• A is the 1st letter. Difference from W (23): We wrap around the alphabet. From W (23) to Z (26) is $+3$. From Z to A (1) is $+1$. Total difference is $3 + 1 = 4$. Alternatively, $(26 - 23) + 1 = 4$ or $(1 - 23) \pmod{26} = -22 \pmod{26} \equiv 4$.

The differences between consecutive letters in KOSWA are consistently +4 (considering wrap-around).

3. QUYCG

• Q is the 17th letter.
• U is the 21st letter. Difference: $21 - 17 = 4$.
• Y is the 25th letter. Difference: $25 - 21 = 4$.
• C is the 3rd letter. Difference from Y (25): From Y (25) to Z (26) is $+1$. From Z to C (3) is $+3$. Total difference is $1 + 3 = 4$. Alternatively, $(26 - 25) + 3 = 4$ or $(3 - 25) \pmod{26} = -22 \pmod{26} \equiv 4$.
• G is the 7th letter. Difference from C (3): $7 - 3 = 4$.

The differences between consecutive letters in QUYCG are consistently +4 (considering wrap-around).

4. VZDHN

• V is the 22nd letter.
• Z is the 26th letter. Difference: $26 - 22 = 4$.
• D is the 4th letter. Difference from Z (26): From Z (26) to D (4) is $+4$. Alternatively, $(4 - 26) \pmod{26} = -22 \pmod{26} \equiv 4$.
• H is the 8th letter. Difference: $8 - 4 = 4$.
• N is the 14th letter. Difference: $14 - 8 = 6$.

The differences between consecutive letters in VZDHN are +4, +4, +4, and +6.

Conclusion

Based on the analysis, the letter clusters BFJNR, KOSWA, and QUYCG all follow a pattern where each consecutive letter is obtained by adding 4 to the positional value of the previous letter (with wrap-around from Z to A). The letter cluster VZDHN follows this pattern for the first three differences (+4, +4, +4) but the last difference is +6.

Therefore, VZDHN is the letter cluster that is different from the others.

Revision Table: Letter Cluster Patterns

Additional Information on Letter Series Problems

Letter series and letter cluster problems are common in reasoning sections of exams. They test your ability to identify patterns based on:

• Positional value of letters (A=1, B=2, ...).
• Differences or sums of positional values.
• Skipping a fixed number of letters.
• Vowel or consonant patterns.
• Reverse alphabetical order or mirror images of letters.
• Combinations of these patterns.

Solving these problems effectively requires familiarity with the alphabet and practice in quickly calculating positional differences and identifying sequences.