In the word CHAIRS, 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 sequence?

Difficulty: Easy

Correct Answer: 2

Explanation:


Introduction / Context:
This is an alphabet test question in which you need to count special letter pairs in a given word. The word is CHAIRS. You must identify those pairs of letters where the number of letters between the two letters in the word is equal to the number of letters between them in the normal alphabetical order. This type of problem checks attention to detail and ability to track positions in both the word and the alphabet sequence.


Given Data / Assumptions:

  • Word: C H A I R S.
  • We use the standard English alphabet: A, B, C, D, and so on up to Z.
  • A pair is formed by taking two letters in the word in the same order as they appear.
  • We must count letters between that pair in the word and letters between them in the alphabet.
  • If the counts are equal, that pair satisfies the condition.


Concept / Approach:
To solve such questions, we can follow a systematic method. First, write the positions of each letter in the word. Then, for each pair, count how many letters lie between them in the word. Next, note the alphabetical positions of the same letters and count how many letters lie between them in the alphabet. If both counts are equal, we count that pair. Careful counting avoids missing pairs or double counting. We only consider the direction of letters as they appear in the word, not reversing them.


Step-by-Step Solution:
Step 1: Write the word with positions: C(1), H(2), A(3), I(4), R(5), S(6).Step 2: Consider the pair C and A. In the word, there is one letter between them (H). In the alphabet, C is the third letter and A is the first; between A and C there is exactly one letter, B. So word gap and alphabet gap are both one. This pair satisfies the condition.Step 3: Consider the pair R and S. In the word, R is at position 5 and S at position 6, so there are zero letters between them. In the alphabet, R and S are consecutive letters, so there are also zero letters between them. This pair also satisfies the condition.Step 4: Check other pairs quickly. For example, C and H have zero letters between in the word but four letters between them in the alphabet. Similar mismatches occur for pairs such as H and I or A and R. None of these satisfy the requirement.Step 5: Conclude that only two pairs, C–A and R–S, meet the condition.


Verification / Alternative check:
If desired, list all possible pairs systematically and compare gaps. Doing so confirms that the only matching pairs are C with A and R with S. Therefore, the correct count is two. Double checking prevents the common error of either overlooking R–S or miscounting the gaps for other pairs such as H–I, which are consecutive in the alphabet but are separated by one letter in the word.


Why Other Options Are Wrong:

  • Option b (3) assumes one extra pair that does not actually meet the condition.
  • Option c (1) means only one of the correct pairs is noticed, which is incomplete.
  • Option d (4) suggests severe overcounting of pairs.
  • Option e (0) would mean that no pair satisfies the condition, which contradicts our careful counting.


Common Pitfalls:
Common mistakes include counting letters from the wrong end of the alphabet, confusing the order of letters in the word, or forgetting that we count letters between the two letters rather than including them. Another pitfall is assuming that any consecutive letters in the word must satisfy the condition without checking the alphabet gap. A systematic and careful comparison avoids these errors.


Final Answer:
There are 2 such pairs of letters in the word CHAIRS.

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