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.
PURE : IDGT :: COOL : VJJM :: LIPS : ?

The correct answer is MPIF.

To solve this letter-cluster analogy, let us analyze the pattern governing the relationship between the pairs of letter-clusters.

Step 1: Analyze the first pair (PURE : IDGT)

First, write down the letters of "PURE" in reverse order: E - R - U - P.
Now, find the opposite (opposite position in the alphabet) letter for each of these reversed letters:

• Opposite of E is I? No, let's check standard alphabetical position or reverse letter pairs (A↔Z, B↔Y, C↔X, etc.):
Standard opposite pairs:
P ↔ K
U ↔ F
R ↔ I
E ↔ V
Notice the opposite letters of PURE are K, F, I, V.
If we reverse the order of these opposite letters (K, F, I, V), we get: V, I, F, K.
Let's examine how IDGT relates to PURE:

Alternatively, look at the position numbers (A=1, B=2, ..., Z=26):
P (16), U (21), R (18), E (5)
I (9), D (4), G (7), T (20)

Let's check the sum of positions for corresponding letters from the end or start:
P (16) + T (20) = 36
U (21) + G (7) = 28
R (18) + D (4) = 22
E (5) + I (9) = 14

Notice the pattern when reading "PURE" in reverse order (E, R, U, P) compared to "IDGT" (I, D, G, T):
• E (5) + 4 = I (9)
Wait, 5 + 4 = 9 (I)
R (18) -> D (4) : 18 - 14 = 4 (D)
U (21) -> G (7) : 21 - 14 = 7 (G)
P (16) -> T (20) : 16 + 4 = 20 (T)

Let's check opposite letters with shift:
P (16) ↔ K (11) -> 11 - 2 = 9 (I)? No, let's check opposite letters of the word reversed:
Reversed "PURE" is E, R, U, P.
Opposite letter pairs (sum of positional values = 27):
• Opposite of E (5) = V (22)
• Opposite of R (18) = I (9)
• Opposite of U (21) = F (6)
• Opposite of P (16) = K (11)

Now consider subtracting 2, +1, or shifting:
Wait! Let's check "COOL : VJJM"
C (3), O (15), O (15), L (12)
V (22), J (10), J (10), M (13)

Take the opposite letters of "COOL":
• Opposite of C (3) = X (24)
• Opposite of O (15) = L (12)
• Opposite of O (15) = L (12)
• Opposite of L (12) = O (15)

Reverse these opposite letters (O, L, L, X):
• O (15) - 2 = M (13)? Or reverse order (V, J, J, M):
• Opposite of L (last letter of COOL) = O (15) -> O - 2 = M (13)? Wait, VJJM in reverse is M, J, J, V.
• Opposite of C (3) = X (24) -> 24 - 2 = 22 (V)
• Opposite of O (15) = L (12) -> 12 - 2 = 10 (J)
• Opposite of O (15) = L (12) -> 12 - 2 = 10 (J)
• Opposite of L (12) = O (15) -> 15 - 2 = 13 (M)

Let's test this exact rule on "PURE":
1. Find the opposite letter of each letter in the word (where Letter + Opposite = 27):
• P (16) ↔ K (11)
• U (21) ↔ F (6)
• R (18) ↔ I (9)
• E (5) ↔ V (22)

2. Subtract 2 from the positional value of each opposite letter:
• K (11) - 2 = 9 → I
• F (6) - 2 = 4 → D
• I (9) - 2 = 7 → G
• V (22) - 2 = 20 → T

Combining these letters gives: IDGT. This matches the first pattern perfectly!

Step 2: Apply the rule to "LIPS"

1. Find the opposite letter of each letter in "LIPS":
• L (12) ↔ O (15)
• I (9) ↔ R (18)
• P (16) ↔ K (11)
• S (19) ↔ H (8)

2. Subtract 2 from the positional value of each opposite letter:
• O (15) - 2 = 13 → M
• R (18) - 2 = 16 → P
• K (11) - 2 = 9 → I
• H (8) - 2 = 6 → F

Combining the resulting letters yields MPIF.