In the word VITREOUS, all the consonants are first arranged alphabetically and then all the vowels are arranged alphabetically after them. In this new arrangement, which letter will be second to the right of the fourth letter from the left?

Introduction / Context:
This problem combines letter classification (vowels and consonants) with alphabetical ordering and positional reasoning. The word VITREOUS must be rearranged by first ordering its consonants alphabetically, followed by all its vowels also in alphabetical order. After creating this new word, we must locate a letter defined by its relative position from the left and then from the right of that position.

Given Data / Assumptions:
- Word: VITREOUS.
- Consonants: V, T, R, S.
- Vowels: I, E, O, U.
- New arrangement rule: all consonants in alphabetical order first, then all vowels in alphabetical order.
- We must find the letter that is second to the right of the fourth letter from the left in this new arrangement.

Concept / Approach:
The solution involves three clear stages: separating consonants and vowels, sorting each group alphabetically, and concatenating them to form the new word. Once that is done, we identify the fourth letter from the left and count two positions to the right to find the desired letter. Careful indexing ensures that we do not miscount positions in the new sequence.

Step-by-Step Solution:
Step 1: List consonants and vowels: consonants are V, T, R, S; vowels are I, E, O, U. Step 2: Arrange consonants alphabetically: R, S, T, V. Step 3: Arrange vowels alphabetically: E, I, O, U. Step 4: Form the new word by placing consonants first and vowels after them: R S T V E I O U. Step 5: Label positions from the left: 1 R, 2 S, 3 T, 4 V, 5 E, 6 I, 7 O, 8 U. Step 6: The fourth letter from the left is V at position 4. Step 7: Second to the right of this letter means move two places to the right, from position 4 to position 6. Step 8: The letter at position 6 is I. Therefore, the required letter is I.

Verification / Alternative check:
To verify, confirm that no consonant or vowel has been omitted or misclassified. The original word VITREOUS clearly contains four consonants and four vowels, making the reconstructed 8 letter sequence consistent. Recount positions from the left to ensure that the fourth letter is V and that positions five and six are E and I. This double check confirms that I is indeed two steps to the right of V in the final arrangement.

Why Other Options Are Wrong:
- "S" is the second letter from the left and not second to the right of the fourth letter.
- "T" is the third letter from the left and lies to the left, not to the right, of V.
- "E" is at position 5, only one place to the right of V, not two places.
None of these alternatives satisfies the positional requirement relative to the fourth letter from the left.

Common Pitfalls:
Mistakes often arise from mixing up consonants and vowels, or from sorting them incorrectly. Another common error is counting only one position to the right when the question asks for the second to the right. Writing all steps clearly and marking positions avoids these issues. Practising similar classification and rearrangement problems builds confidence in handling more complex alphabet arrangements in reasoning exams.

Final Answer:
In the new arrangement of VITREOUS, the letter that is second to the right of the fourth letter from the left is I.