In the letter analogy "RM : XG :: ER : ____", which pair of letters correctly completes the pattern?

Introduction / Context:
This question is a letter based analogy where two letters are transformed into another pair of letters using a hidden rule. You are given the pair "RM : XG" and asked to apply the same rule to the pair "ER" to find the missing letters. Such questions test your ability to work with the numerical positions of letters in the English alphabet and to recognise consistent shifts.

Given Data / Assumptions:

• First example pair: RM becomes XG.
• Second incomplete pair: ER becomes an unknown pair.
• Alphabet positions: A = 1, B = 2, ..., Z = 26.
• Exactly the same transformation must be applied to both pairs.

Concept / Approach:
To solve this, convert letters to their numerical positions and see how they are shifted. R is the 18th letter and M is the 13th letter. X is the 24th letter and G is the 7th letter. From R to X, the position increases by 6. From M to G, the position decreases by 6, since 13 minus 6 equals 7. So the rule for the pair seems to be: first letter moves forward by 6 positions, second letter moves backward by 6 positions. We then apply the same pattern to E and R.

Step-by-Step Solution:

Step 1: Write numerical positions for RM. R = 18, M = 13. Step 2: Write positions for XG. X = 24, G = 7. Step 3: Compare positions. For the first letter: 18 + 6 = 24, so R moves forward 6 places to X. For the second letter: 13 minus 6 = 7, so M moves backward 6 places to G. Step 4: Write positions for ER. E = 5, R = 18. Step 5: Apply the rule. First letter: 5 + 6 = 11, which is K. Second letter: 18 minus 6 = 12, which is L. Step 6: Combine these to get KL as the answer.

Verification / Alternative check:
Quickly check all options. PK would mean 5 becomes P (position 16) which is a shift of +11, not +6. LK would place letters in the wrong order. PL and KM also do not correspond to the exact shifts of +6 for the first letter and minus 6 for the second letter. Only KL is consistent with the transformation discovered from the example pair RM : XG.

Why Other Options Are Wrong:
PK, LK, PL and KM all involve different numeric shifts that are not equal in magnitude to +6 for the first position and minus 6 for the second position. Since analogy questions demand that exactly the same rule be applied to both pairs, any option that breaks that rule must be rejected. The reasoning shows that KL alone preserves the pattern.

Common Pitfalls:
Many students try to guess based on how similar pairs look, instead of converting letters into numbers. Another common mistake is to apply the shift in only one direction (for example, moving both letters forward) without checking both letters carefully. Writing out the positions and performing clear additions and subtractions helps avoid confusion.

Final Answer:
The correct completion of the analogy is "RM : XG :: ER : KL".