Letter Cluster Analogy Solution

The question asks to identify the relationship between the first letter cluster and the second, and apply that same relationship to find the missing fourth cluster.

Analyzing the Pattern

Let's examine the relationship between the first pair (GKP : FHK) and the second pair (BJS : AGN).

• First Pair (GKP : FHK):
  • G is the 7th letter, F is the 6th. Difference: $7 - 6 = 1$.
  • K is the 11th letter, H is the 8th. Difference: $11 - 8 = 3$.
  • P is the 16th letter, K is the 11th. Difference: $16 - 11 = 5$.
  The pattern is: subtract 1 from the first letter's position, 3 from the second, and 5 from the third.
• Second Pair (BJS : AGN):
  • B is the 2nd letter, A is the 1st. Difference: $2 - 1 = 1$.
  • J is the 10th letter, G is the 7th. Difference: $10 - 7 = 3$.
  • S is the 19th letter, N is the 14th. Difference: $19 - 14 = 5$.
  This pair follows the same pattern: subtract 1, 3, and 5 from the letter positions.

Applying the Pattern to DIX

Now, we apply the established pattern (subtract 1, 3, 5) to the letter cluster DIX:

• First Letter (D): D is the 4th letter. Subtract 1: $4 - 1 = 3$. The 3rd letter is C.
• Second Letter (I): I is the 9th letter. Subtract 3: $9 - 3 = 6$. The 6th letter is F.
• Third Letter (X): X is the 24th letter. Subtract 5: $24 - 5 = 19$. The 19th letter is S.

Resulting Cluster

Combining the resulting letters gives the cluster CFS.

Therefore, DIX : CFS follows the same relationship.