In the letter pairs AG, WA, ET and IQ, find the odd pair based on the sum of the alphabetical positions of the letters.

Introduction / Context:
This odd one out item uses pairs of letters to hide a simple numeric pattern. By converting letters to their positions in the English alphabet and adding these positions, we can reveal a rule that three pairs follow and one pair breaks. Such questions are common in verbal and logical reasoning tests and require both observation and a basic understanding of alphabet positions.

Given Data / Assumptions:
The four letter pairs are AG, WA, ET and IQ. We use the standard mapping A = 1, B = 2, C = 3, and so on up to Z = 26. We compute the sum of the positions of both letters in each pair. We look for a pattern that is common to three pairs and absent in one pair.

Concept / Approach:
A straightforward strategy is to convert each letter to its numeric position and then calculate the sum. Sometimes the sums form a simple sequence, such as consecutive numbers, or share a common property like being all even or all odd. Here, three pairs produce sums that are consecutive integers, while one pair gives a sum that does not fit that sequence. The pair with the non matching sum is the odd one out.

Step-by-Step Solution:
Step 1: For AG, A = 1 and G = 7, so the sum is 1 + 7 = 8. Step 2: For WA, W = 23 and A = 1, so the sum is 23 + 1 = 24. Step 3: For ET, E = 5 and T = 20, so the sum is 5 + 20 = 25. Step 4: For IQ, I = 9 and Q = 17, so the sum is 9 + 17 = 26. Step 5: Now compare the sums: AG gives 8, WA gives 24, ET gives 25 and IQ gives 26. Step 6: The sums 24, 25 and 26 are three consecutive integers, forming a neat sequence, while 8 is far away from this range. Step 7: Therefore, AG is the pair whose letter position sum does not fit into the consecutive sequence 24, 25, 26 and so it is the odd one out.

Verification / Alternative check:
As a quick verification, write only the sums in numeric order: 8, 24, 25 and 26. You can clearly see a block of three consecutive numbers 24, 25, 26 and a single value 8 that stands apart. There is no way to reorder the pairs to make AG fit into the same consecutive pattern as the other three, which confirms that AG is the intended odd pair.

Why Other Options Are Wrong:
WA is not the odd pair because the sum of its letter positions, 24, lies in the consecutive block 24, 25, 26. ET is not the odd pair because its sum of positions, 25, continues the consecutive sequence. IQ is not the odd pair because its sum, 26, completes the consecutive run 24, 25, 26. AG is the odd pair because its sum, 8, is far outside this consecutive group and does not share the same pattern.

Common Pitfalls:
Learners sometimes focus on the distance between the two letters in each pair, such as the difference in positions, and miss the simpler sum pattern. Another pitfall is to look for complex coding schemes when a basic arithmetic approach is enough. To avoid such mistakes, always try both the difference and the sum of letter positions when dealing with alphabet based reasoning questions.

Final Answer:
The letter pair whose position sum does not belong to the consecutive sequence 24, 25, 26 and is therefore the odd one out is AG.