Letter Cluster Pairs Analysis

The task is to identify the letter-cluster pair that differs from the others based on a specific relationship derived from the English alphabetical order. We need to find the outlier among MD-GK, KB-EJ, QH-KO, and OF-IM.

Understanding the Alphabetical Relationship Pattern

We assign numerical positions to letters (A=1, B=2, ..., Z=26). The pattern likely involves a consistent transformation from the first letter of the first cluster to the first letter of the second cluster, and similarly for the second letters.

Let the pair be represented as $L1L2$-$L3L4$. We investigate the relationship based on the positional values:

• Transformation for the first letter: $Pos(L3) = Pos(L1) - k_1$
• Transformation for the second letter: $Pos(L4) = Pos(L2) + k_2$

Where $k_1$ and $k_2$ are constants for the group.

Detailed Examination of Each Pair

Option 1: MD-GK

Analysis:

• First Letter: M (13) to G (7). The change is $7 - 13 = -6$. So, $Pos(L1) \rightarrow Pos(L1) - 6$.
• Second Letter: D (4) to K (11). The change is $11 - 4 = +7$. So, $Pos(L2) \rightarrow Pos(L2) + 7$.

This pair follows the pattern: (Subtract 6, Add 7).

Option 2: KB-EJ

Analysis:

• First Letter: K (11) to E (5). The change is $5 - 11 = -6$. This matches the pattern $Pos(L1) \rightarrow Pos(L1) - 6$.
• Second Letter: B (2) to J (10). The change is $10 - 2 = +8$. This follows $Pos(L2) \rightarrow Pos(L2) + 8$.

This pair deviates because the second letter transformation is +8, not +7.

Option 3: QH-KO

Analysis:

• First Letter: Q (17) to K (11). The change is $11 - 17 = -6$. This matches the pattern $Pos(L1) \rightarrow Pos(L1) - 6$.
• Second Letter: H (8) to O (15). The change is $15 - 8 = +7$. This matches the pattern $Pos(L2) \rightarrow Pos(L2) + 7$.

This pair follows the pattern: (Subtract 6, Add 7).

Option 4: OF-IM

Analysis:

• First Letter: O (15) to I (9). The change is $9 - 15 = -6$. This matches the pattern $Pos(L1) \rightarrow Pos(L1) - 6$.
• Second Letter: F (6) to M (13). The change is $13 - 6 = +7$. This matches the pattern $Pos(L2) \rightarrow Pos(L2) + 7$.

This pair follows the pattern: (Subtract 6, Add 7).

Identifying the Outlier Pair

Three pairs (MD-GK, QH-KO, OF-IM) consistently follow the rule where the first letter's position decreases by 6 ($L1 \rightarrow L1 - 6$) and the second letter's position increases by 7 ($L2 \rightarrow L2 + 7$).

The pair KB-EJ adheres to the first letter rule ($K \rightarrow E$, i.e., $11 \rightarrow 5$, which is $-6$) but deviates in the second letter rule. For KB-EJ, the second letter changes from B (2) to J (10), representing a shift of $+8$ ($2 \rightarrow 10$), not the $+7$ seen in the other pairs.

Therefore, KB-EJ is the letter-cluster pair that does not belong to the group.