In this alphabet to single letter analogy, AD is related to N through a position based code; using the same idea, choose the correct letter that completes the pattern: AD : N :: BD : ?

Introduction / Context:
This problem is an alphabet coding analogy where a pair of letters maps to a single letter. The pair AD is coded as N, and you must determine how BD will be coded under the same rule. These questions test your ability to work with alphabet positions, two digit numbers and their mapping to letters.

Given Data / Assumptions:

• The alphabet runs from A = 1 to Z = 26.
• The pair AD is mapped to the single letter N.
• The same rule must be applied to BD to find the correct resulting letter.
• The answer must be one of P, X, Y or Z.

Concept / Approach:
Since two letters are mapped to just one letter, a common technique is to encode the two positions as a two digit number, then interpret that number as the position of the resulting letter. For example, if A is 1 and D is 4, you can place their positions side by side to make the number 14. The 14th letter of the alphabet is N, which matches the given code. If this interpretation holds, then BD should be converted to its position based two digit number and mapped the same way.

Step-by-Step Solution:
Step 1: Find the positions of A and D. A is 1 and D is 4.Step 2: Form the two digit number from these positions. Combining 1 and 4 gives 14.Step 3: Determine the 14th letter of the alphabet. Counting forward, the 14th letter is N.Step 4: This confirms that AD is coded as N by mapping positions 1 and 4 to the number 14 and then to the 14th letter.Step 5: Now apply the same idea to BD. B is the 2nd letter, and D is the 4th letter.Step 6: Combine these positional values to form the two digit number 24.Step 7: The 24th letter of the alphabet is X.Step 8: Therefore BD is coded as X under the same rule, which matches option B.

Verification / Alternative check:
We can verify that no other reasonable interpretation fits the given code AD mapped to N. If we added positions, 1 plus 4 would give 5, which maps to E, not N. If we multiplied them, 1 times 4 would give 4, which maps to D. The unique pattern that explains N is the two digit number 14 interpreted as a letter position. Using the same method on BD naturally yields 24, or X.

Why Other Options Are Wrong:
Option A, P, is the 16th letter and would require the number 16, not 24. Option C, Y, is the 25th letter, and option D, Z, is the 26th. None of these values arise from the concatenation of positions 2 and 4. Hence they do not match the coding logic that is clearly established by the example pair.

Common Pitfalls:
Some candidates try to sum the positions or look for average values without checking whether those operations actually lead to the given code N. Others may miscount letter positions beyond M. The best practice is to test proposed rules on the example pair first and only then apply a rule that exactly reproduces the known mapping.

Final Answer:
The letter that completes the analogy correctly is X, so option B is correct.