Letter Cluster Analogy Question Explained

The objective is to find the letter-cluster pair that deviates from a pattern shared by the other three pairs. The pattern relies on the standard English alphabetical sequence. We need to analyze the relationship between the two letter clusters presented in each option.

Letter Pair Relationships Analysis

To uncover the underlying logic, we will assign numerical positions to each letter based on its place in the alphabet (A=1, B=2, ..., Z=26). Then, we'll examine how the letters in the first cluster of each pair transform to form the second cluster.

Solution Steps Analysis

Let's break down each option:

1. Pair HZ-EA

• The first cluster is HZ. The alphabetical positions are H = 8 ($P(H)=8$) and Z = 26 ($P(Z)=26$).
• The second cluster is EA. The alphabetical positions are E = 5 ($P(E)=5$) and A = 1 ($P(A)=1$).
• Now, let's find the difference in positions for each letter:
• First letter transformation: H (8) to E (5). The shift is $P(E) - P(H) = 5 - 8 = -3$.
• Second letter transformation: Z (26) to A (1). The shift is $P(A) - P(Z) = 1 - 26 = -25$. In modular arithmetic (wrapping around the alphabet), $-25$ is equivalent to $+1$, since $-25 + 26 = 1$. So, the shift is $+1 \pmod{26}$.
• The pattern observed for HZ-EA is (Shift of -3, Shift of +1 mod 26).

2. Pair LD-LE

• The first cluster is LD. The alphabetical positions are L = 12 ($P(L)=12$) and D = 4 ($P(D)=4$).
• The second cluster is LE. The alphabetical positions are L = 12 ($P(L)=12$) and E = 5 ($P(E)=5$).
• Let's find the difference in positions:
• First letter transformation: L (12) to L (12). The shift is $P(L) - P(L) = 12 - 12 = 0$.
• Second letter transformation: D (4) to E (5). The shift is $P(E) - P(D) = 5 - 4 = +1$.
• The pattern observed for LD-LE is (Shift of 0, Shift of +1).

3. Pair ZR-WS

• The first cluster is ZR. The alphabetical positions are Z = 26 ($P(Z)=26$) and R = 18 ($P(R)=18$).
• The second cluster is WS. The alphabetical positions are W = 23 ($P(W)=23$) and S = 19 ($P(S)=19$).
• Let's find the difference in positions:
• First letter transformation: Z (26) to W (23). The shift is $P(W) - P(Z) = 23 - 26 = -3$.
• Second letter transformation: R (18) to S (19). The shift is $P(S) - P(R) = 19 - 18 = +1$.
• The pattern observed for ZR-WS is (Shift of -3, Shift of +1).

4. Pair JB-GC

• The first cluster is JB. The alphabetical positions are J = 10 ($P(J)=10$) and B = 2 ($P(B)=2$).
• The second cluster is GC. The alphabetical positions are G = 7 ($P(G)=7$) and C = 3 ($P(C)=3$).
• Let's find the difference in positions:
• First letter transformation: J (10) to G (7). The shift is $P(G) - P(J) = 7 - 10 = -3$.
• Second letter transformation: B (2) to C (3). The shift is $P(C) - P(B) = 3 - 2 = +1$.
• The pattern observed for JB-GC is (Shift of -3, Shift of +1).

Odd One Out Identification

Let's summarize the patterns we found:

• HZ-EA: (-3, +1 mod 26)
• LD-LE: (0, +1)
• ZR-WS: (-3, +1)
• JB-GC: (-3, +1)

Three pairs (HZ-EA, ZR-WS, and JB-GC) follow a consistent rule: the first letter shifts backward by 3 positions, and the second letter shifts forward by 1 position.

The pair LD-LE does not conform to this rule, as its first letter shift is 0, not -3.

Conclusion

Based on the analysis, the letter-cluster pair LD-LE is the one that does not belong to the group.