Difficulty: Medium
Correct Answer: RXC
Explanation:
Introduction / Context:
This question is based on alphabet positions and letter patterns. Each option is a group of three letters. In three of the groups, the letters follow a consistent numerical spacing pattern in the alphabet. In one group, this pattern breaks. Identifying this difference requires converting each letter to its alphabet position and analysing the jumps between consecutive letters.
Given Data / Assumptions:
Concept / Approach:
A common pattern in letter-group questions is that the second letter is a fixed number of positions ahead of the first, and the third letter is the same number of positions ahead of the second. Often the difference is 2, 3, 4 or 6. To find the odd group, we compute the differences between letters in each option and see which group does not share the same constant step value as the others. We also may need to consider circular movement from Z back to A for some groups.
Step-by-Step Solution:
Step 1: Convert letters in MSY to positions. M = 13, S = 19 and Y = 25. The differences are 19 - 13 = 6 and 25 - 19 = 6. So MSY follows a +6, +6 pattern. Step 2: Convert letters in KQW to positions. K = 11, Q = 17 and W = 23. The differences are 17 - 11 = 6 and 23 - 17 = 6. KQW also follows a +6, +6 pattern. Step 3: Convert letters in DJP to positions. D = 4, J = 10 and P = 16. The differences are 10 - 4 = 6 and 16 - 10 = 6. DJP again follows a +6, +6 pattern. Step 4: Convert letters in RXC to positions. R = 18, X = 24 and C = 3. The difference from R to X is 24 - 18 = 6, which fits +6. To go from X to C, we can think in two ways. Directly, 3 - 24 = -21. If we use circular counting from Z = 26 back to A = 1, moving forward from X (24) by 6 positions gives 30, which corresponds to 30 - 26 = 4, that is D, not C. So the second jump is not +6; it is effectively -21 or +? depending on direction, but it is not +6. Step 5: Summarise. MSY, KQW and DJP all have consistent forward jumps of +6 between each pair of letters. RXC has the first jump as +6 but the second jump is not +6 in any straightforward forward counting. Step 6: Conclude that RXC is the odd group because it breaks the repeated +6 stepping pattern that the other three groups follow.
Verification / Alternative check:
We can try to see whether RXC might follow some different but common pattern, such as alternating directions or equal backward steps. R to X is forward, while X to C is a big backward jump, so it does not mirror the harmonious forward stepping seen in other options. No alternate simple pattern unites RXC with the remaining three groups. The cleanest and most symmetric rule is that each group should feature two equal positive steps of 6, which RXC does not satisfy.
Why Other Options Are Wrong:
MSY is not odd because it fits the pattern of +6 and +6 jumps. KQW also has differences of +6 and +6 between consecutive letters. DJP similarly follows the same +6 spacing, so all three belong to one consistent category. Since they all satisfy the same simple rule, none of them can be considered the odd-man-out. Only RXC breaks the pattern and therefore must be the answer.
Common Pitfalls:
One frequent mistake is to look only at the first two letters and ignore the relationship between the second and third letters. This can cause a student to overlook the fact that RXC breaks the pattern on the second jump. Another common issue is to forget about circular wrapping from Z to A or to misapply it. When checking possible forward movement from X by 6 steps, careful counting shows it would land on D, not C. Being precise with alphabet positions and differences avoids these errors.
Final Answer:
The odd group of letters is RXC, because only this group does not show two equal forward jumps of 6 positions between its consecutive letters, unlike MSY, KQW and DJP.
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