Analyzing the Letter Arrangement for Specific Consonant Patterns

The question asks us to find the number of consonants in the given arrangement that satisfy two conditions simultaneously: they must be immediately preceded by a vowel and immediately followed by a consonant.

Understanding Vowels and Consonants

First, let's identify the vowels and consonants in the English alphabet:

• Vowels: A, E, I, O, U
• Consonants: All other letters (B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z)

Examining the Given Arrangement

The arrangement provided is: C B T A E X F I M K E U V N X O D

We need to look for a pattern that looks like this: Vowel - Consonant - Consonant, where the middle 'Consonant' is the letter we are counting.

Step-by-Step Analysis

Let's go through the arrangement letter by letter and check for the required pattern:

1. C B T: No vowel precedes C. B is preceded by a consonant (C). T is preceded by a consonant (B).
2. A E X F:
   • 'A' is a vowel.
   • 'E' is a vowel.
   • 'X' is a consonant. It is preceded by 'E' (a vowel) and followed by 'F' (a consonant). This fits the pattern Vowel - Consonant - Consonant (E - X - F). So, 'X' is one such consonant.
   • 'F' is a consonant. It is preceded by 'X' (a consonant).
3. I M K:
   • 'I' is a vowel.
   • 'M' is a consonant. It is preceded by 'I' (a vowel) and followed by 'K' (a consonant). This fits the pattern Vowel - Consonant - Consonant (I - M - K). So, 'M' is another such consonant.
   • 'K' is a consonant. It is preceded by 'M' (a consonant).
4. E U V N:
   • 'E' is a vowel.
   • 'U' is a vowel.
   • 'V' is a consonant. It is preceded by 'U' (a vowel) and followed by 'N' (a consonant). This fits the pattern Vowel - Consonant - Consonant (U - V - N). So, 'V' is the third such consonant.
   • 'N' is a consonant. It is preceded by 'V' (a consonant).
5. X O D:
   • 'X' is a consonant. It is preceded by 'N' (a consonant).
   • 'O' is a vowel.
   • 'D' is a consonant. It is preceded by 'O' (a vowel) but not followed by another consonant (it's the end of the arrangement).

Identifying the Consonants

Based on the analysis, the consonants that are immediately preceded by a vowel and immediately followed by a consonant are:

• X (between E and F)
• M (between I and K)
• V (between U and N)

Final Count

Counting these identified consonants, we find there are 3 such letters in the given arrangement.