In the letter analogy "IJ : PR :: ____ : SU", which pair of letters correctly completes the pattern?

Introduction / Context:
This analogy involves a fixed shift in the positions of letters in the alphabet. The pair "IJ : PR" indicates that the letters I and J are transformed into P and R using a consistent rule. You must detect this rule and then apply it to an unknown pair so that the result is SU. This type of question checks your ability to handle forward shifts and to work backward from an output to an input.

Given Data / Assumptions:

• First pair: IJ is mapped to PR.
• Second pair: unknown pair is mapped to SU.
• Alphabet positions: A = 1, B = 2, ..., Z = 26.
• The same shift rule must work for both letters of each pair.

Concept / Approach:
First, convert letters in IJ and PR into numbers. I is the 9th letter, J the 10th, P the 16th, and R the 18th. From I to P the position increases by 7 (9 + 7 = 16). From J to R the position increases by 8 (10 + 8 = 18). So the transformation uses two different shifts: +7 applied to the first letter and +8 applied to the second letter. For the pair that must become SU, we reverse the process and subtract these amounts to get the original letters.

Step-by-Step Solution:

Step 1: Find numerical positions. I = 9, J = 10, P = 16, R = 18. Step 2: Compute shifts. 9 + 7 = 16, so the first letter moves forward by 7. 10 + 8 = 18, so the second letter moves forward by 8. Step 3: For SU, write the positions: S = 19, U = 21. Step 4: Reverse the transformation for the first letter. 19 minus 7 = 12, which is L. Step 5: Reverse the transformation for the second letter. 21 minus 8 = 13, which is M. Step 6: Combine them to get LM, so the missing pair is LM.

Verification / Alternative check:
Check that if we now apply the original shifts to LM we really get SU. L is the 12th letter. 12 + 7 = 19, which is S. M is the 13th letter. 13 + 8 = 21, which is U. This confirms that LM transforms to SU under the same rule that converts IJ to PR. None of the other options, when shifted by +7 and +8 in this way, yield SU.

Why Other Options Are Wrong:
If you try IJ again, adding 7 and 8 gives PR, not SU. EF and LI similarly do not produce SU under the same shift pattern. MN would become T V when shifted (+7 and +8), not S U. Therefore, all options except LM break the required transformation rule and cannot be correct in the analogy.

Common Pitfalls:
Many students expect the same shift to be applied to both letters and miss patterns where the first and second letters use different shifts. Another common mistake is to only work forward from the given input instead of working backward from the known output. In such cases, working in reverse often makes the structure more obvious.

Final Answer:
The correct completion is "IJ : PR :: LM : SU".