In this letter analogy, ART is related to BSU. Using the same pattern, which group of letters should complete the analogy ART : BSU :: MRV : ?

Introduction / Context:
This analogy question involves a consistent forward shift in the alphabet for each letter in a three letter group. The pair ART : BSU indicates that each letter in the second group is obtained by adding the same positive number of positions to the corresponding letter in the first group. The same rule must then be applied to MRV to identify the correct related group.

Given Data / Assumptions:
First pair: ART : BSU. Second pair: MRV : ?. All letters are capital letters from A to Z. The same transformation is applied position wise.

Concept / Approach:
We convert each letter to its numerical position in the alphabet and compute the difference between corresponding letters in ART and BSU. If the difference is +1 consistently for each position, we can infer that the pattern is add 1 to every letter. We then apply this simple rule to MRV to obtain the answer. This technique of translating letters to numbers is a standard method in letter analogy questions.

Step-by-Step Solution:
Step 1: Convert ART to positions. A = 1, R = 18, T = 20. Step 2: Convert BSU to positions. B = 2, S = 19, U = 21. Step 3: Find the differences. 1 to 2 is +1. 18 to 19 is +1. 20 to 21 is +1. Therefore each letter in ART is shifted one position forward to produce BSU. Step 4: Apply the same +1 rule to MRV. M = 13, R = 18, V = 22. 13 + 1 = 14, which is N. 18 + 1 = 19, which is S. 22 + 1 = 23, which is W. So MRV becomes NSW.

Verification / Alternative check:
To verify, we apply the reverse operation to NSW. N is 14, so 14 minus 1 is 13, which is M. S is 19, so 19 minus 1 is 18, which is R. W is 23, so 23 minus 1 is 22, which is V. This confirms that MRV and NSW are linked by a uniform plus one shift, exactly paralleling the relationship between ART and BSU.

Why Other Options Are Wrong:
KFT does not result from adding one to each letter in MRV and shows unrelated shifts. MFG uses an entirely different set of letters that do not maintain the positions relative to M, R, and V. NRV modifies only the first letter and leaves the others unchanged, breaking the consistent shift pattern. MTX modifies letters by unequal amounts and therefore fails to follow a uniform +1 rule.

Common Pitfalls:
Learners may forget to check all three positions and instead base their answer on the first letter alone. This can be dangerous because some distractor options are designed to match the pattern partially. Always verify the transformation for every corresponding letter in the pair and ensure that the same rule applies uniformly across positions for both the example pair and the target pair.

Final Answer:
The group of letters that correctly completes the analogy is NSW.