In the letter pair series BD, HJ, NP, which of the following pairs correctly completes the pattern as the next term?

Introduction / Context:
This question presents a series of two letter pairs: BD, HJ, NP and asks you to find the next pair in the sequence. It belongs to the alphabet series category where the positions of letters in the English alphabet follow a clear arithmetic pattern. Understanding how both the first and second letters of each pair progress helps in predicting the next pair correctly. Such items test basic number sense combined with alphabetical positions.

Given Data / Assumptions:

• Given pairs: BD, HJ, NP.
• We use positions of letters in the English alphabet (A as 1, B as 2, and so on up to Z as 26).
• We must identify the pattern for the first letters and the second letters separately.
• Options: TU, TV, SV, SU, WX.

Concept / Approach:
For letter pair series, a systematic approach is to convert letters to their numeric positions and observe differences. If the first letters follow a sequence with a certain common difference and the second letters follow a similar or related pattern, we can apply the same rule to generate the next pair. Here, both letters in each pair appear to increment by the same constant number across pairs, which suggests an arithmetic progression in their positions.

Step-by-Step Solution:
Step 1: Write the positions of the first letters. B is 2, H is 8, and N is 14. Step 2: Calculate the differences between these positions. From 2 to 8 is a jump of +6, and from 8 to 14 is also a jump of +6. So, the first letters increase by 6 each time. Step 3: To find the next first letter, add 6 to 14. This gives 20, which corresponds to the letter T. Step 4: Now look at the second letters. D is 4, J is 10, and P is 16. Step 5: Again, compute the differences: 4 to 10 is +6, and 10 to 16 is +6. So the second letters also increase by 6 each time. Step 6: Add 6 to 16 to get 22, which corresponds to the letter V. Step 7: Therefore, the next pair in the series must be T (20) and V (22), that is, "TV".

Verification / Alternative check:
We can quickly re check our pattern: BD has positions (2,4), HJ is (8,10), NP is (14,16). In each case the difference between the two letters in the pair is 2. In "TV", positions are (20,22), and the difference is again 2, consistent with earlier pairs. At the same time, each pair jumps 6 positions forward from the previous pair for both letters. This double confirmation assures us that "TV" fits perfectly in the sequence.

Why Other Options Are Wrong:
"TU" has letters at positions 20 and 21, where the internal difference is only 1, breaking the pattern of difference 2 within each pair and also not matching the +6 external increment for the second letter.
"SV" starts with 19 instead of 20, so the first letter difference from N would be +5, not +6.
"SU" also starts at 19 and ends at 21, giving an internal difference of 2 but external jumps of +5, which do not follow the established pattern.
"WX" corresponds to 23 and 24, which would require a jump of +9 from the previous pair, not +6, and the internal difference is only 1, again breaking the pattern.

Common Pitfalls:
One common error is to only look at the internal difference between the two letters of each pair and ignore how the pairs progress from one to the next. Another mistake is not converting letters to numbers and instead trying to guess by visual impression. Using position numbers makes patterns far clearer and avoids confusion. Always check both dimensions: progression of first letters and progression of second letters.

Final Answer:
The correct pair that completes the series is TV.