Question Details

In the word ‘BONAFIDE’, how many pairs of letters have the same number of letters between them (both forward and backward direction) as in the alphabetical series?

Options

A

Four

B

Two

C

One

D

Three

E

More than Four

Show Answer

Correct Answer :

Option E

More than Four

More than Four

Solution :

To find the number of pairs of letters in the word "BONAFIDE" that have the same number of letters between them as in the English alphabetical series, we examine the letters in both the forward (left-to-right) and backward (right-to-left) directions.

Let us first list the letters of the word "BONAFIDE" along with their respective positions in the word:
1: B, 2: O, 3: N, 4: A, 5: F, 6: I, 7: D, 8: E

Now, we compare the position differences between any two letters in the word with their positional differences in the standard alphabetical order:
A = 1, B = 2, C = 3, D = 4, E = 5, F = 6, G = 7, H = 8, I = 9, J = 10, K = 11, L = 12, M = 13, N = 14, O = 15, P = 16, etc.

Let's check the pairs in the forward direction:
- B to F: Letters between them in the word are O, N, A (3 letters). In the alphabet: B (2) and F (6) have C, D, E between them (3 letters). So, (B, F) is a valid pair.
- B to I: Letters between them in the word are O, N, A, F (4 letters). In the alphabet: B (2) and I (9) have C, D, E, F, G, H between them (6 letters). This is not a pair.
- O to N: Letters between them in the word is 0. In the alphabet: N and O are adjacent. Since we look in both directions (forward/backward), the pair (O, N) or (N, O) is a valid pair.
- N to F: Letters between them in the word is A (1 letter). In the alphabet: F (6) and N (14) have 7 letters between them.
- A to F: Letters between them in the word is 0. In the alphabet: A (1) and F (6) have 4 letters between them.
- F to I: Letters between them in the word is 0. In the alphabet: F (6) and I (9) have G, H between them (2 letters).
- F to D: Backward check: In the word, F (5th) and D (7th) have I (1 letter) between them. In the alphabet: D (4) and F (6) have E (1 letter) between them. So, (F, D) is a valid pair.
- D to E: Letters between them in the word is 0. In the alphabet: D (4) and E (5) are adjacent. So, (D, E) is a valid pair.

Let's check the pairs in the backward direction:
- E to I: In the word, E (8th) and I (6th) have D (1 letter) between them. In the alphabet: E (5) and I (9) have F, G, H (3 letters) between them.
- D to I: In the word, D (7th) and I (6th) have 0 letters between them. In the alphabet: D (4) and I (9) have 4 letters.
- I to N: In the word, I (6th) and N (3rd) have F, A (2 letters) between them. In the alphabet: I (9) and N (14) have J, K, L, M (4 letters) between them.
- A to D: In the word, A (4th) and D (7th) have F, I (2 letters) between them. In the alphabet: A (1) and D (4) have B, C (2 letters) between them. So, (A, D) is a valid pair.
- A to E: In the word, A (4th) and E (8th) have F, I, D (3 letters) between them. In the alphabet: A (1) and E (5) have B, C, D (3 letters) between them. So, (A, E) is a valid pair.
- N to O: As analyzed above, N (3rd) and O (2nd) are adjacent in both the word and the alphabet. So, (N, O) is a valid pair.

Let us compile the list of all matching pairs found:
1. (B, F) - letters between them in word: O, N, A (3); in alphabet: C, D, E (3).
2. (O, N) - letters between them in word: none (0); in alphabet: none (0).
3. (F, D) - letters between them in word: I (1); in alphabet: E (1).
4. (D, E) - letters between them in word: none (0); in alphabet: none (0).
5. (A, D) - letters between them in word: F, I (2); in alphabet: B, C (2).
6. (A, E) - letters between them in word: F, I, D (3); in alphabet: B, C, D (3).

Since we have found 6 pairs, which is greater than four, the correct option is "More than Four".

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