In the following letter code analogy, CM is related to P by a positional rule in the alphabet. Using the same rule, PM is related to which of the following single letters?

Introduction / Context:
This question involves converting a pair of letters into a single letter using their positions in the English alphabet. You are told that CM maps to P, and you must then determine what PM maps to using the same rule. These types of analogies check your comfort with letter position arithmetic and pattern recognition under a coded format.

Given Data / Assumptions:
- First input pair: CM.
- First output: P.
- Second input pair: PM.
- Options are letters F, E, D and C.
- We assume a simple numerical relationship based on alphabetical positions rather than arbitrary assignment.

Concept / Approach:
Assign numerical positions to letters: A is 1, B is 2, ..., Z is 26. For CM, C has position 3 and M has position 13. Notice that the sum 3 + 13 equals 16, and the 16th letter of the alphabet is P. Therefore, CM is mapped to P by adding the positions of the two letters and converting the sum back to a letter. We apply the same rule to PM.

Step-by-Step Solution:
Step 1: Convert C and M to their positions, 3 and 13. Step 2: Add these positions: 3 + 13 = 16. Step 3: Identify the 16th letter of the alphabet, which is P. This confirms the rule for the first mapping. Step 4: Now process PM. P has position 16 and M has position 13. Step 5: Add 16 and 13 to get 29. Step 6: Because the alphabet has 26 letters, we convert 29 back into a valid position by subtracting 26. So 29 minus 26 equals 3. Step 7: The 3rd letter of the alphabet is C, so PM maps to C.

Verification / Alternative check:
Check that the same modular logic works for CM. The sum 3 + 13 is 16, which does not exceed 26, so no wraparound is needed and P is directly valid. For PM, wraparound is required because 29 is greater than 26. Taking 29 minus 26 to get 3 is a standard modular arithmetic step when working with letter positions. The resulting letter C appears exactly among the options and matches the rule consistently.

Why Other Options Are Wrong:
Options F, E and D correspond to positions 6, 5 and 4. None of these values equals 3, which is the reduced position we obtain from 16 + 13. Selecting any of them would break the sum based mapping that works perfectly for CM. Therefore they cannot be correct under a single consistent rule.

Common Pitfalls:
One common mistake is forgetting to wrap around after 26, leading candidates to pick 29 as if it were a valid letter position. Another is trying to use different operations for the second pair, like subtraction instead of addition, which violates the requirement of a uniform rule. Always apply the same numeric rule and remember that letter positions cycle after 26.

Final Answer:
CM maps to P by adding the letter positions, so PM maps to position 3 and therefore to the letter C.