Based on the English alphabetical order, three of the following four letter-clusters are alike in a certain way and thus form a group. Which letter-cluster DOES NOT belong to that group?
(Note: The odd one out is not based on the number of consonants/vowels or their position in the letter-cluster.)

The correct answer is OSN.

To solve this logical reasoning question, let us analyze the pattern followed by the letters in each letter-cluster based on their positions in the English alphabetical order.

Let us write down the numerical positions of the letters in the English alphabet:
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.

Now, let us examine the relationship between the letters in each option:

1. GKE:
G = 7
K = 11
E = 5
Pattern: 7 + 4 = 11, and 11 - 6 = 5.
(First letter + 4 = Second letter, Second letter - 6 = Third letter)

2. NRL:
N = 14
R = 18
L = 12
Pattern: 14 + 4 = 18, and 18 - 6 = 12.
(First letter + 4 = Second letter, Second letter - 6 = Third letter)

3. LPJ:
L = 12
P = 16
J = 10
Pattern: 12 + 4 = 16, and 16 - 6 = 10.
(First letter + 4 = Second letter, Second letter - 6 = Third letter)

4. OSN:
O = 15
S = 19
N = 14
Pattern: 15 + 4 = 19, but 19 - 5 = 14.
Here, the difference between the second and third letter is -5 instead of -6.

Therefore, OSN does not follow the (+4, -6) pattern and is the odd letter-cluster out.