In the word CREATIVE, how many pairs of letters have as many letters between them in the word as they have between them in the English alphabet sequence?

Introduction / Context:
This is a classic letter pair counting question that appears frequently in reasoning and banking exams. It tests your ability to track relative positions of letters within a word and compare them with positions in the alphabet. You need to be precise while counting the number of letters between two given letters in both the word and the alphabet. Careful systematic checking helps you avoid missing valid pairs or counting invalid ones.

Given Data / Assumptions:
The given word is CREATIVE. We need to consider all possible pairs of letters taken in the order they appear from left to right. For each pair, we count the letters between them in the word and the number of letters between those same letters in the standard A to Z alphabet. A pair is considered valid if these two counts are equal. The question finally asks for the total number of such valid pairs present in the word CREATIVE.

Concept / Approach:
Assign each letter in the alphabet a numeric position from 1 to 26. For any two letters, the number of letters between them in the alphabet is the absolute difference of their positions minus one. Within the word, the number of letters between two positions is the index difference minus one. We must check every pair in the word and see where these two counts match. Doing this systematically ensures that no valid pair is overlooked.

Step-by-Step Solution:
Write CREATIVE with positions: C(1), R(2), E(3), A(4), T(5), I(6), V(7), E(8). First consider C and E: in the word they are at positions 1 and 3, so there is 1 letter between them (R). In the alphabet, C and E also have one letter between them (D). So C E is a valid pair. Next consider A and E at positions 4 and 8: there are 3 letters between them in the word (T, I, V). In the alphabet between A and E we have B, C and D, also 3 letters. So A E is a second valid pair. Now look at T and V at positions 5 and 7: between them in the word is one letter (I). In the alphabet between T and V there is U, which is exactly one letter. So T V is a third valid pair. Checking all other possible pairs in the word shows that no further pair has matching counts.

Verification / Alternative check:
A quick verification method is to list all pairs explicitly and jot down two numbers next to each: the gap in the word and the gap in the alphabet. When you do this for CREATIVE, only the three pairs C E, A E and T V show equal gaps. Another cross check is to focus on visually promising pairs, such as those whose letters are alphabetically close or obviously far apart, and calculate their differences carefully. Both approaches converge to the same conclusion that exactly three pairs meet the condition. This confirms the total without relying on guesswork.

Why Other Options Are Wrong:
Option 1 and Option 2 underestimate the count because they ignore at least one of the valid pairs. Option 4 and More than four overestimate the count and include pairs where the word gap and alphabet gap do not match. For example, C and R are adjacent in the word but are far apart in the alphabet, so they do not qualify. Only the three identified pairs satisfy the precise numerical condition, making 3 the only correct total. All other option values conflict with the detailed pair by pair analysis.

Common Pitfalls:
A frequent mistake is to count only from left to right and forget that any pair of letters within the word must be checked, not just neighbouring ones. Another error is miscounting the number of letters between two positions in the alphabet, especially when the letters are near the start or end. Some students also confuse the requirement and compare the raw alphabet positions instead of comparing gaps. To avoid these errors, work methodically, maybe using a small table where you record each pair and its two gap counts. This disciplined approach greatly reduces the chance of missing or inventing pairs.

Final Answer:
There are exactly 3 pairs of letters in CREATIVE that have the same number of letters between them in the word and in the alphabet sequence.