Solving Letter-Cluster Analogy Problems

This question is a letter-cluster analogy problem. We are given two pairs of letter-clusters (MOTHER : SGKXTS and SIMPLE : FNSQNY) that share a specific relationship or pattern. We need to identify this pattern and then apply it to the fifth letter-cluster (DELIGHT) to find the related cluster from the given options.

Decoding the Relationships: MOTHER to SGKXTS and SIMPLE to FNSQNY

Let's analyze the relationship between the first pair, MOTHER and SGKXTS, and the second pair, SIMPLE and FNSQNY. Both original words (MOTHER, SIMPLE) and their corresponding clusters (SGKXTS, FNSQNY) have 6 letters.

We can try looking for letter shifts based on their alphabetical positions (A=1, B=2, ..., Z=26). Let's look at the letters in order:

• M (13) → S (19): +6
• O (15) → G (7): -8
• T (20) → K (11): -9
• H (8) → X (24): +16 (or -10)
• E (5) → T (20): +15 (or -6)
• R (18) → S (19): +1

This sequence of shifts (+6, -8, -9, +16, +15, +1) seems inconsistent. Let's try another approach.

Let's consider if the pattern involves reversing the original word.

The reverse of MOTHER is REHTOM.

Let's see if there is a pattern between the letters of REHTOM and SGKXTS:

• R (18) → S (19): +1
• E (5) → G (7): +2
• H (8) → K (11): +3
• T (20) → X (24): +4
• O (15) → T (20): +5
• M (13) → S (19): +6

This shows a consistent pattern! The letters of the reversed first word are shifted by +1, +2, +3, +4, +5, +6 respectively to get the second letter-cluster.

Let's test this pattern on the second pair: SIMPLE and FNSQNY.

The reverse of SIMPLE is ELPMIS.

Now, apply the shifts (+1, +2, +3, +4, +5, +6) to ELPMIS:

• E (+1) → F
• L (+2) → N
• P (+3) → S
• M (+4) → Q
• I (+5) → N
• S (+6) → Y

The resulting cluster is FNSQNY, which matches the given second cluster. The pattern is confirmed: Reverse the first word, then apply increasing shifts (+1, +2, +3, ...) to its letters.

Applying the Pattern to DELIGHT

Now, we apply the same pattern to the third word, DELIGHT.

1. Reverse the word DELIGHT.

The reverse of DELIGHT is THGILED.

2. Apply the progressive shifts to the letters of THGILED. Since DELIGHT has 7 letters, the shifts will be +1, +2, +3, +4, +5, +6, +7.

• T (+1) → \(T \xrightarrow{+1} U\)
• H (+2) → \(H \xrightarrow{+2} J\)
• G (+3) → \(G \xrightarrow{+3} J\)
• I (+4) → \(I \xrightarrow{+4} M\)
• L (+5) → \(L \xrightarrow{+5} Q\)
• E (+6) → \(E \xrightarrow{+6} K\)
• D (+7) → \(D \xrightarrow{+7} K\)

Combining these shifted letters, we get the cluster UJJMQKK.

Comparing with Options

Let's compare our derived cluster UJJMQKK with the given options:

• Option 1: UJJMQJJ
• Option 2: VJJMQKK
• Option 3: UJJMQKK
• Option 4: THGILED

Our calculated cluster UJJMQKK matches Option 3.

Therefore, the letter-cluster related to DELIGHT in the same way is UJJMQKK.

Revision Table: Letter Positions

Understanding the alphabetical position of letters is crucial for solving coding-decoding and analogy problems.

Additional Information: Letter Coding and Analogy

Letter coding and analogy questions test your ability to identify patterns in the rearrangement or transformation of letters. Common patterns include:

• Letter Shifting: Each letter is shifted by a fixed number of positions forward or backward in the alphabet.
• Progressive Shifting: The amount of shift increases or decreases for successive letters.
• Reversal: The order of letters in the word is reversed.
• Pairing/Grouping: Patterns might apply to pairs of letters or groups within the word.
• Vowel/Consonant Based: Different rules might apply to vowels and consonants.
• Position Based: The rule depends on the letter's position in the word (e.g., first letter, last letter, middle letter).

Solving these problems often requires trial and error, systematically testing different pattern types until a consistent rule is found across the given examples. Once the pattern is identified, it can be applied to the new word.