Select the option that is related to the fifth letter-cluster in the same way as the second letter-cluster is related to the first letter-cluster and the fourth letter-cluster is related to the third letter-cluster.
FREE : GTHI :: GAPS : HCSW :: SOAR : ?

The correct answer is TQDV.

To solve this letter-cluster analogy, let us analyze the pattern connecting the pairs of letter-clusters step-by-step.

1. First Pair: FREE : GTHI

Let us look at the positional values of each letter in the English alphabet:

F (6) → G (7) : +1
R (18) → T (20) : +2
E (5) → H (8) : +3
E (5) → I (9) : +4

The pattern adds +1, +2, +3, and +4 to the alphabet positions of the letters sequentially.

2. Second Pair: GAPS : HCSW

Let us check if the same pattern applies to the second pair:

G (7) → H (8) : +1
A (1) → C (3) : +2
P (16) → S (19) : +3
S (19) → W (23) : +4

The rule (+1, +2, +3, +4) holds true.

3. Applying the Rule to SOAR:

Now, let us apply this sequential increment rule to the fifth letter-cluster SOAR:

S (19) + 1 = 20 → T
O (15) + 2 = 17 → Q
A (1) + 3 = 4 → D
R (18) + 4 = 22 → V

Combining these resulting letters gives TQDV.