Identifying the Odd Letter Cluster

The question requires us to find the letter cluster that is different from the others among the given options. The strategy is to find a common pattern or relationship between the letters within the clusters DWKO, QJUF, HSYB, and GTXC, and then identify the one cluster that does not follow this pattern.

Assigning Numerical Values to Letters

A common method for solving such problems is to assign numerical values to each letter based on its position in the English alphabet (A=1, B=2, ..., Z=26). Let's find these values for the letters in each cluster:

• D = 4, W = 23, K = 11, O = 15
• Q = 17, J = 10, U = 21, F = 6
• H = 8, S = 19, Y = 25, B = 2
• G = 7, T = 20, X = 24, C = 3

Analyzing Letter Cluster Sums

Let's calculate the sum of the alphabetical position values for each letter cluster. This might reveal a pattern.

We will calculate the sum '$S$' for each cluster, where '$S = \text{pos}(L_1) + \text{pos}(L_2) + \text{pos}(L_3) + \text{pos}(L_4)$', with '$L_1, L_2, L_3, L_4$' being the letters in the cluster.

Step-by-Step Calculation for Each Cluster

Let's perform the sum calculation for each option:

Identifying the Odd One Out

By examining the sums calculated above:

• The sum of the letter positions for DWKO is 53.
• The sum of the letter positions for QJUF is 54.
• The sum of the letter positions for HSYB is 54.
• The sum of the letter positions for GTXC is 54.

Three of the letter clusters (QJUF, HSYB, GTXC) have the same sum of alphabetical positions (54). The cluster DWKO has a different sum (53). Therefore, DWKO is the odd one out based on this numerical pattern.