In the letter number analogy "CD : IP :: EB : ____", which pair of letters correctly completes the pattern?

Introduction / Context:
This analogy involves a fixed forward shift in the positions of letters in the English alphabet. The pair "CD : IP" shows that the letters C and D are changed into I and P according to a hidden numerical rule. You must identify this rule and then apply it to EB to find the correct resulting pair. This checks your comfort with alphabet positions and simple arithmetic on those positions.

Given Data / Assumptions:

• First pair: CD is mapped to IP.
• Second pair: EB is mapped to an unknown pair.
• Alphabet positions: A = 1, B = 2, C = 3, D = 4, ..., Z = 26.
• The same transformation must apply to both letters within each pair.

Concept / Approach:
Write the letters as numbers. C is position 3, D is position 4. I is position 9, P is position 16. From 3 to 9, the shift is +6. From 4 to 16, the shift is +12. So the pattern is: first letter moves forward by 6 positions, second letter moves forward by 12 positions. We then apply this same rule to E and B to generate the new letters.

Step-by-Step Solution:

Step 1: Convert the letters in CD to positions. C = 3 and D = 4. Step 2: Convert the letters in IP to positions. I = 9 and P = 16. Step 3: Calculate the shift for the first letter. 3 + 6 = 9, so the first letter is shifted forward by 6 positions. Step 4: Calculate the shift for the second letter. 4 + 12 = 16, so the second letter is shifted forward by 12 positions. Step 5: Now consider EB. E = 5 and B = 2. Step 6: Apply the same shifts. First letter: 5 + 6 = 11, which is K. Second letter: 2 + 12 = 14, which is N. Step 7: Combine these letters to obtain KN as the answer.

Verification / Alternative check:
If we test the other options using the reverse transformation, they do not match EB. For example, for HI, H is 8 and I is 9. Shifting H backward by 6 gives 2 (B), and shifting I backward by 12 gives a negative position, which does not correspond cleanly to E. Similarly, YA and XY require very different shifts that do not match the consistent pattern derived from CD : IP. Only KN follows the exact plus 6 and plus 12 rule when traced back.

Why Other Options Are Wrong:
HI, YA, XY, and KP all fail when you try to apply the same shift pattern in reverse. They either give positions outside the valid range or give letters that do not correspond to E and B. Since the analogy is based on fixed numerical shifts, any deviation from this pattern means that the option is not correct.

Common Pitfalls:
One pitfall is to assume the same amount of shift for both letters and look for a simple constant, which does not work here. Another common error is to guess visually similar letter pairs without doing the numeric checks. Converting letters to their numerical positions and writing out the arithmetic makes these patterns far easier to see and greatly reduces guesswork.

Final Answer:
The analogy is completed as "CD : IP :: EB : KN".