Select the related pair of letters from the given alternatives: JS is to QH as VW is to which letter pair?

Introduction / Context:
This is a letter pair analogy. The pair JS is related to QH using a positional relationship in the alphabet, and you must determine which option forms a similar relationship with the pair VW. The trick here is to look at how far apart the two letters of each pair are and how this difference changes from the first pair to the second pair in the analogy.

Given Data / Assumptions:

• The first pair is JS and the related pair is QH.
• The second starting pair is VW and we must find its related pair.
• The answer options for the second pair are HM, PQ, JQ, and ED.
• Alphabet positions are taken as A = 1, B = 2, ..., Z = 26.
• We assume that a consistent relation between the first and second letters within each pair is mirrored across the analogy.

Concept / Approach:
Instead of only looking at the absolute positions of letters, we focus on the difference between the two letters in each pair. For JS, we compute the difference between S and J. For QH, we compute the difference between H and Q. The pattern turns out to be that the difference in the first pair is reversed in sign in the second pair. We then apply the same idea to VW to see which candidate pair has the opposite difference.

Step-by-Step Solution:
Step 1: Convert J and S to positions. J is 10 and S is 19. Step 2: Compute the difference within the first pair JS: 19 minus 10 equals +9. Step 3: Convert Q and H to positions. Q is 17 and H is 8. Step 4: Compute the difference within QH: 8 minus 17 equals -9. Step 5: Observe that the magnitude of the difference is the same (9), but the sign is reversed from +9 to -9. Step 6: Now consider the pair VW. V is 22 and W is 23, so the difference is 23 minus 22 = +1. Step 7: We need a new pair whose internal difference is -1 to mirror this pattern. Step 8: Check each option. For ED, E is 5 and D is 4. The difference is 4 minus 5 = -1, which matches the required reversed difference.

Verification / Alternative check:
Check that none of the other options have a difference of -1. For HM, the difference is 13 minus 8 = +5. For PQ, the difference is 17 minus 16 = +1. For JQ, the difference is 17 minus 10 = +7. Only ED gives -1 as required. Furthermore, we can summarise the pattern as: in the example, the second pair in the analogy has the same magnitude of difference as the first pair but with reversed direction. JS has +9, QH has -9. VW has +1, so its partner must have -1, which ED satisfies perfectly.

Why Other Options Are Wrong:
HM, PQ, and JQ all have positive internal differences, so they fail the sign reversal requirement. PQ even duplicates the +1 difference that exists in VW, but the rule demands that the difference be reversed, not repeated. Using any of these options would break the symmetry between the example pair and the new pair, so they cannot be correct under a strict analogy interpretation.

Common Pitfalls:
A typical mistake is to look for a direct shift in letter values from J to Q and from S to H, and then try to apply the same shifts to V and W. That approach leads to a different answer that does not appear among the options. When that happens, it is a sign that a different relation might be in play. Considering internal differences rather than cross pair shifts helps prevent this confusion and leads to the correct ED option.

Final Answer:
Because JS has an internal difference of +9 and QH has an internal difference of -9, VW with a difference of +1 must correspond to a pair with an internal difference of -1, namely ED.