Understanding Letter-Cluster Analogies

This question asks us to find a relationship between pairs of letter clusters and apply that relationship to a new cluster. The pattern established between the first two pairs (KITE : IFQA and TIRE : RFOA) must be the same pattern applied to the third cluster (DIRE) to find the missing cluster.

Let's analyze the relationship between the letters in the first pair: KITE and IFQA.

• The first letter of KITE is K, and the first letter of IFQA is I. The difference in their alphabetical position is $K (11^{th}) - I (9^{th}) = -2$.
• The second letter of KITE is I, and the second letter of IFQA is F. The difference in their alphabetical position is $I (9^{th}) - F (6^{th}) = -3$.
• The third letter of KITE is T, and the third letter of IFQA is Q. The difference in their alphabetical position is $T (20^{th}) - Q (17^{th}) = -3$.
• The fourth letter of KITE is E, and the fourth letter of IFQA is A. The difference in their alphabetical position is $E (5^{th}) - A (1^{st}) = -4$.

So, the pattern for the first pair KITE : IFQA is a positional shift of -2, -3, -3, -4 for each corresponding letter.

Verifying the Pattern with the Second Pair: TIRE and RFOA

Let's apply the discovered pattern (-2, -3, -3, -4) to the second letter cluster, TIRE, and see if it results in RFOA.

• First letter: T ($20^{th}$) shifted by -2 is R ($18^{th}$).
• Second letter: I ($9^{th}$) shifted by -3 is F ($6^{th}$).
• Third letter: R ($18^{th}$) shifted by -3 is O ($15^{th}$).
• Fourth letter: E ($5^{th}$) shifted by -4 is A ($1^{st}$).

Applying the pattern (-2, -3, -3, -4) to TIRE gives RFOA. This confirms the pattern is consistent across the first two analogy pairs.

Applying the Pattern to the Third Cluster: DIRE

Now, we apply the same pattern (-2, -3, -3, -4) to the letter cluster DIRE to find the missing cluster.

• First letter: D ($4^{th}$) shifted by -2 is B ($2^{nd}$).
• Second letter: I ($9^{th}$) shifted by -3 is F ($6^{th}$).
• Third letter: R ($18^{th}$) shifted by -3 is O ($15^{th}$).
• Fourth letter: E ($5^{th}$) shifted by -4 is A ($1^{st}$).

Applying the pattern (-2, -3, -3, -4) to DIRE results in the letter cluster BFOA.

This matches option 1.

Step-by-Step Derivation

The missing letter-cluster is BFOA.

Conclusion on Letter-Cluster Relationship

The analogy is based on a consistent positional shift of letters in the alphabet. The first letter shifts back by 2 positions, the second by 3, the third by 3, and the fourth by 4 positions.

Revision Table: Letter Analogies

Understanding letter analogies often involves checking for patterns based on:

• Positional shift (forward or backward)
• Skipping letters
• Reversing the order of letters
• Vowel/consonant patterns
• Combination of these patterns

Additional Information: Solving Analogy Questions

To effectively solve letter-cluster analogy questions in competitive exams, follow these steps:

1. Carefully observe the relationship between the first pair of letter clusters. Look for patterns in letter positions, order, or types (vowel/consonant).
2. Formulate a hypothesis about the pattern based on the first pair.
3. Test the hypothesis on the second pair of letter clusters. If the pattern holds true for the second pair, you've likely found the correct rule.
4. Apply the established pattern to the third letter cluster to derive the missing one.
5. Check your derived cluster against the given options.