Four letter-clusters have been given, out of which three are alike in some manner and one is different. Select the letter-cluster that is different.

The correct option is GTQ.

To find the odd letter-cluster, let us analyze the relationships between the letters in each cluster. A common pattern in letter-cluster questions involves examining the English alphabetical positions of the letters or their relationships as opposite pairs (where the sum of the positions of two letters is 27).

Let's write down the alphabetical positions of all English letters for reference:
A=1, B=2, C=3, D=4, E=5, F=6, G=7, H=8, I=9, J=10, K=11, L=12, M=13, N=14, O=15, P=16, Q=17, R=18, S=19, T=20, U=21, V=22, W=23, X=24, Y=25, Z=26.

Let's analyze each option step-by-step:

1. SPK:
- The positions are S = 19, P = 16, K = 11.
- Let's check the relationship between the first and third letters: S (19) and K (11). Their sum is 19 + 11 = 30.
- Let's check the relationship between the second and third letters: P (16) and K (11). They are opposite pairs because 16 + 11 = 27 (P and K are opposites).
- Let's check the difference between the first and second letters: S (19) to P (16) is a decrease of 3 (19 - 3 = 16).

2. JGT:
- The positions are J = 10, G = 7, T = 20.
- Let's check the relationship between the first and second letters: J (10) to G (7) is a decrease of 3 (10 - 3 = 7).
- Let's check the relationship between the second and third letters: G (7) and T (20). They are opposite pairs because 7 + 20 = 27 (G and T are opposites).

3. PMN:
- The positions are P = 16, M = 13, N = 14.
- Let's check the relationship between the first and second letters: P (16) to M (13) is a decrease of 3 (16 - 3 = 13).
- Let's check the relationship between the second and third letters: M (13) and N (14). They are opposite pairs because 13 + 14 = 27 (M and N are opposites).

4. GTQ:
- The positions are G = 7, T = 20, Q = 17.
- Let's check the relationship between the first and second letters: G (7) to T (20) is an increase of 13 (7 + 13 = 20), which does not follow the -3 pattern.
- Let's check the relationship between the second and third letters: T (20) and Q (17). The sum is 20 + 17 = 37, which is not 27 (T and Q are not opposite pairs).

Conclusion:
In the clusters SPK, JGT, and PMN, the first letter is shifted by -3 to get the second letter, and the second and third letters are alphabetical opposites (their positional values sum to 27). The cluster GTQ does not follow this pattern.