Solving Letter Cluster Analogy Questions

This question asks us to find a relationship between letter clusters, similar to how the first cluster relates to the second and the third cluster relates to the fourth. We need to apply the same relationship to the fifth cluster to find the missing one.

The given relationships are:

• BET : UXM
• SYP : LRI
• HOX : ?

Let's analyze the first pair to find the pattern.

Analyzing the First Letter Cluster Pair: BET to UXM

We can analyze the relationship between the letters by looking at their positions in the English alphabet. Let's assign numerical values to each letter (A=1, B=2, ..., Z=26).

• B is the 2nd letter. U is the 21st letter.
• E is the 5th letter. X is the 24th letter.
• T is the 20th letter. M is the 13th letter.

Now let's look at the difference in positions for each corresponding letter:

• For the first letter: From B (2) to U (21). The difference is $21 - 2 = 19$. Alternatively, considering a wrap-around from Z back to A, $2 - 26 = -24$. To reach 21 from 2, we could think of subtracting: $2 - 7 = -5$. If we wrap around (add 26), $-5 + 26 = 21$. This matches U. So, $-7$ seems plausible.
• For the second letter: From E (5) to X (24). The difference is $24 - 5 = 19$. Using the $-7$ pattern: $5 - 7 = -2$. Adding 26 for wrap-around: $-2 + 26 = 24$. This matches X. The $-7$ pattern holds.
• For the third letter: From T (20) to M (13). The difference is $13 - 20 = -7$. This directly matches the $-7$ pattern.

The pattern discovered is to subtract 7 from the alphabetical position of each letter. When the result is less than or equal to 0, add 26 to get the wrapped-around position.

Let's summarize the rule:

New Position = (Original Position - 7) modulo 26 (if 0 or negative, add 26)

Using standard position values (1-26):

• B(2) $\xrightarrow{-7}$ $2 - 7 = -5 \xrightarrow{+26} 21$ (U)
• E(5) $\xrightarrow{-7}$ $5 - 7 = -2 \xrightarrow{+26} 24$ (X)
• T(20) $\xrightarrow{-7}$ $20 - 7 = 13$ (M)

The rule seems consistent for the first pair.

Verifying the Pattern with SYP to LRI

Let's apply the same rule to the second pair: SYP to LRI.

• S is the 19th letter.
• Y is the 25th letter.
• P is the 16th letter.

Applying the $-7$ rule:

• S(19) $\xrightarrow{-7}$ $19 - 7 = 12$. The 12th letter is L.
• Y(25) $\xrightarrow{-7}$ $25 - 7 = 18$. The 18th letter is R.
• P(16) $\xrightarrow{-7}$ $16 - 7 = 9$. The 9th letter is I.

The resulting cluster is LRI, which matches the given second cluster. The $-7$ pattern is confirmed.

Applying the Pattern to HOX

Now, let's apply the same pattern to the fifth letter-cluster, HOX, to find the missing cluster.

• H is the 8th letter.
• O is the 15th letter.
• X is the 24th letter.

Applying the $-7$ rule to each letter:

• H(8) $\xrightarrow{-7}$ $8 - 7 = 1$. The 1st letter is A.
• O(15) $\xrightarrow{-7}$ $15 - 7 = 8$. The 8th letter is H.
• X(24) $\xrightarrow{-7}$ $24 - 7 = 17$. The 17th letter is Q.

The resulting letter cluster is AHQ.

Comparing with Options

Let's check the options to see which one matches AHQ.

• Option 1: NVE
• Option 2: AHQ
• Option 3: BHQ
• Option 4: MVE

The calculated cluster AHQ matches Option 2.

Conclusion

By analyzing the relationship between the letter positions in the given pairs, we found a consistent pattern of subtracting 7 from the position of each letter. Applying this pattern to the letter cluster HOX results in the cluster AHQ.

Revision Table: Letter Cluster Analogy

Additional Information: Types of Letter Series and Analogies

Letter series and analogy problems are common in logical reasoning and verbal ability tests. They assess your ability to identify patterns in sequences or pairs of letters.

Common types of patterns include:

• Position-Based Patterns: Relationships based on the alphabetical position of letters, like the example above (adding or subtracting a fixed number, or a changing number).
• Difference-Based Patterns: Looking at the difference between consecutive letters in a series or between corresponding letters in an analogy pair.
• Skip-Letter Patterns: Skipping a fixed number of letters between consecutive terms.
• Vowel/Consonant Patterns: Based on the arrangement of vowels and consonants.
• Reverse Alphabetical Order: Patterns moving backward through the alphabet.
• Combination Patterns: A mix of two or more simple patterns.

To solve these problems, it's often helpful to write down the alphabetical positions of the letters and look for mathematical or logical relationships between these numbers.