In the following analogy, a missing pair of letters must be found: ? is to LM as QR is to WX. Which pair of letters correctly completes the analogy?

Introduction / Context:
This question gives you a letter pair analogy with one pair missing. You are shown that QR is related to WX, and you must find the pair that relates to LM in the same way. Such problems test your ability to identify fixed positional shifts of letters across the alphabet and then apply that pattern consistently.

Given Data / Assumptions:
- Known second pair: QR and WX.
- Unknown first pair: ? and LM.
- Options: CD, EF, FG and TU.
- We assume that each letter in QR is shifted by a fixed amount to produce WX and that the same shift is used from the missing pair to LM.

Concept / Approach:
Convert letters into positions in the alphabet. Q is 17, R is 18, W is 23 and X is 24. Moving from Q to W is a shift of +6 (17 to 23) and from R to X is also +6 (18 to 24). Therefore the pattern is that both letters are shifted six steps forward. To create an analogy, the unknown pair must be such that applying a +6 shift to each of its letters results in L and M respectively.

Step-by-Step Solution:
Step 1: Confirm the shift from QR to WX: 17 to 23 and 18 to 24 show a consistent +6. Step 2: Let the unknown pair be AB, representing some letters X and Y, where X shifted by +6 becomes L and Y shifted by +6 becomes M. Step 3: Convert L and M to positions: L is 12 and M is 13. Step 4: Subtract 6 from each: 12 - 6 = 6 and 13 - 6 = 7. Step 5: The 6th and 7th letters of the alphabet are F and G. Step 6: Thus the missing pair must be FG, because FG shifted forward by 6 positions becomes LM.

Verification / Alternative check:
Check the forward shift: F (6) plus 6 is 12 which is L, and G (7) plus 6 is 13 which is M. This exactly replicates the pattern seen from Q to W and from R to X. No other given option pair, when shifted by +6, results in LM for both letters. This consistency verifies the correctness of FG.

Why Other Options Are Wrong:
Option A CD has letters in positions 3 and 4. When each is increased by 6, they become 9 (I) and 10 (J), not L and M. Option B EF in positions 5 and 6 would map to positions 11 (K) and 12 (L), giving KL instead of LM. Option D TU would map to Z and beyond the alphabet, requiring wraparound and breaking the neat pattern. None of these produce LM under a simple +6 shift.

Common Pitfalls:
A typical mistake is to attempt matching LM directly to QR and WX without checking for the precise shift value. Another error is to ignore that the same numerical difference must apply to both letters in each pair. Writing out letter positions and systematically computing the shift steeply reduces guesswork and errors.

Final Answer:
The only pair which, when each letter is shifted six places forward, produces LM is FG.