In the letter pair series CM, EK, GI, which of the following pairs correctly completes the pattern as the next term?

Introduction / Context:
This is another two letter series question with the terms CM, EK, GI, followed by a missing pair. The series clearly involves changes in both the first and second letters, and the pattern is almost certainly based on arithmetic progressions in the alphabet positions. Recognizing how the letters move forward or backward helps identify the next pair logically.

Given Data / Assumptions:

• Given pairs: CM, EK, GI, ?
• Alphabet positions: C 3, E 5, G 7, M 13, K 11, I 9.
• We must find the next pair from IK, IG, LM, PS, HJ.

Concept / Approach:
We consider the first letters as one sequence and the second letters as another sequence. If each sequence follows a simple arithmetic pattern, such as adding or subtracting a constant each time, we can extend that pattern and obtain the missing letters. Often these patterns move in opposite directions for first and second letters, making the pair progression visually interesting but numerically predictable.

Step-by-Step Solution:
Step 1: Convert the first letters to numeric positions: C is 3, E is 5, and G is 7. Step 2: Determine the differences between these positions. From 3 to 5 is +2, and from 5 to 7 is +2. So the first letters increase by 2 each time. Step 3: Continue the pattern for the first letter. Add 2 to G, which is at position 7, giving 9. The 9th letter is I. Step 4: Convert the second letters to numeric positions: M is 13, K is 11, and I is 9. Step 5: Compute the differences. From 13 to 11 is minus 2, and from 11 to 9 is minus 2. Thus the second letters decrease by 2 each time. Step 6: Apply this to find the next second letter. Subtract 2 from 9 to get 7, which corresponds to G. Step 7: Combine the new first and second letters: I as first and G as second, forming the pair "IG".

Verification / Alternative check:
Writing out the series in numeric form confirms the pattern: CM (3,13), EK (5,11), GI (7,9), IG (9,7). The first coordinate increases by 2 at every step, while the second coordinate decreases by 2 at every step. This consistent pattern leaves no doubt that the next pair must be IG. None of the other options matches the required coordinates of 9 and 7 simultaneously.

Why Other Options Are Wrong:
"IK" uses I as the first letter correctly, but K is 11, which would represent an increase from 9 instead of the expected decrease of 2.
"LM" has first letter L (12) and second letter M (13); neither 12 nor 13 fits the positions 9 and 7 dictated by the pattern.
"PS" gives P as 16 and S as 19, far from the expected next coordinates.
"HJ" reverses the direction of change and does not reflect the combined pattern of plus 2 and minus 2 observed in the series.

Common Pitfalls:
Some students look only at the first letters and conclude that the series may simply be C, E, G, I, which is correct, but fail to check whether the second letters follow an opposite or complementary pattern. Others may guess a pair like IK because it is visually close to GI, without verifying the numeric steps. Always validate patterns for both components of the pair before making a final choice.

Final Answer:
The pair that correctly completes the series is IG.