In the series of letter pairs AN, CP, ER, which of the following pairs correctly continues the pattern as the next term?

Introduction / Context:
The given problem is a letter pair series: AN, CP, ER, followed by a missing pair to be chosen from the options. Many reasoning questions like this rely on simple arithmetic progressions in the alphabet positions of letters. By treating letters as numbers based on their position in the alphabet, we can often discover a neat pattern and extend the sequence correctly.

Given Data / Assumptions:

• Given pairs: AN, CP, ER.
• We use positions A 1, B 2, C 3, and so on up to Z 26.
• We need to find the next pair among options: LY, WJ, VI, GT, HX.

Concept / Approach:
The systematic approach is to examine the pattern among the first letters and among the second letters separately. If both sub sequences show a regular step, we can confidently use that step to find the next pair. The series AN, CP, ER suggests that the first letters are A, C, and E, while the second letters are N, P, and R. Both of these sequences may be following a simple difference pattern in terms of alphabet positions.

Step-by-Step Solution:
Step 1: Write positions of the first letters. A is 1, C is 3, and E is 5. Step 2: Observe that 1 to 3 is a jump of +2 and 3 to 5 is again +2. So the first letters increase by 2 positions each time. Step 3: Continue this pattern. Add 2 to the last first letter E (5). This gives 7, which is the position of G. So the next first letter should be G. Step 4: Now examine the second letters N, P, and R. N is 14, P is 16, and R is 18 in the alphabet. Step 5: From 14 to 16 is +2, and from 16 to 18 is also +2. So the second letter also increases by 2 each time. Step 6: Add 2 to 18 to obtain 20, which is the position of T. Thus the next second letter should be T. Step 7: Put the two letters together. The next pair in the sequence must be G (7) and T (20), forming "GT".

Verification / Alternative check:
We can quickly verify by listing the full sequences. First letters: A, C, E, G show a clear step of plus two. Second letters: N, P, R, T also show the same step. No other option matches G as the first letter and T as the second letter simultaneously. Checking all options, only "GT" satisfies the observed pattern. That makes it the consistent continuation of the given letter pair series.

Why Other Options Are Wrong:
"LY" has first letter L, which is far ahead of E and does not follow a plus two pattern; Y also does not come from R through a step of plus two.
"WJ" has first letter W and second letter J; neither fits the smooth progression visible in the series.
"VI" starts with V and has I as the second letter, again breaking both first and second letter progressions.
"HX" has first letter H which would be plus three from E, and X which does not fit the plus two stepping from R. Thus all these patterns are inconsistent with the earlier terms.

Common Pitfalls:
A common mistake is to try to match options by intuition instead of carefully converting letters to numbers. Another error is to identify a pattern in one position but ignore whether the second position follows the same logic. Always test both first and second letters, and only then choose the option that maintains the pattern across the full series.

Final Answer:
The next pair in the series is GT.