In the word REGIONAL, how many pairs of letters are there such that the number of letters between them in the word is the same as the number of letters between them in the English alphabet when counted in the forward direction?

Introduction / Context:
This problem tests the concept of alphabetical spacing and positional relationships between letters, which is common in alphabet test and reasoning sections of aptitude exams. The task is to examine the word REGIONAL and identify how many pairs of letters satisfy a specific condition relating distances within the word and in the English alphabet. Such questions help evaluate attention to detail and the ability to compare structures in two different sequences simultaneously.

Given Data / Assumptions:

• The given word is REGIONAL.
• Positions in the word are considered from left to right starting at position 1.
• The English alphabet positions are A = 1, B = 2, C = 3, and so on up to Z = 26.
• We count letters between two chosen letters in the word and also letters between the same two letters in alphabetical order moving forward from the first to the second.
• A valid pair is one where the count of letters between them in the word equals the count of letters between them in the alphabet in the same forward direction.

Concept / Approach:
We need to systematically check pairs of letters inside REGIONAL. For every pair, we calculate two quantities. First we count the number of letters between the two letters inside the word. Second we count the number of letters between the same two letters in the English alphabet, moving forwards from the earlier letter to the later one. If these two counts are equal and the alphabetical movement is forward, the pair is considered valid. We then count how many such valid pairs exist.

Step-by-Step Solution:
Step 1: Write REGIONAL with positions: R(1), E(2), G(3), I(4), O(5), N(6), A(7), L(8). Step 2: Consider the letter positions in the alphabet: R = 18, E = 5, G = 7, I = 9, O = 15, N = 14, A = 1, L = 12. Step 3: Check forward pairs systematically. For example, G at position 3 and L at position 8: between them in the word there are 4 letters (I, O, N, A). Between G (7) and L (12) in the alphabet there are also 4 letters (H, I, J, K). This is a valid pair. Step 4: Check other forward pairs such as E to G, E to I, E to O and so on. When we restrict ourselves to forward alphabetical movement (second letter has a higher alphabetical position), only the pair G and L satisfies the condition where the in word spacing equals the alphabetical spacing. Step 5: Any other pair where counts match but alphabetical order is reversed is not accepted as per the forward direction condition in the question wording.

Verification / Alternative check:
We can quickly confirm the answer by listing all possible forward pairs and noting the difference between their positions. Only G at position 3 and L at position 8 provide an equal count of letters in between in both the word and the alphabet when moving from G to L. Since no other forward pair from the word can satisfy this exactly, we can be confident that there is only one valid pair.

Why Other Options Are Wrong:
The option stating that there is no such pair is incorrect because the pair G L clearly satisfies the condition. The options claiming two or three pairs are incorrect because any additional pair either fails the forward alphabetical order requirement or the counts of letters between them do not match in the word and in the alphabet. The option saying more than three such pairs is far from correct because detailed checking shows only a single qualifying pair.

Common Pitfalls:
Candidates often consider both forward and backward alphabetical directions or forget to verify the exact number of letters between the letters. Some students mistakenly count the letters themselves instead of the letters between them. Others rely on intuition and guess that such questions usually have multiple pairs, leading them to choose two or three pairs without systematic checking. Careful comparison of positions is essential to avoid these errors.

Final Answer:
There is exactly one pair of letters in REGIONAL that satisfies the given condition.