Each letter in the word HYDROMETER is changed to the letter preceding it in the English alphabetical order and then all the letters thus formed are arranged in alphabetical order. Which of the following letters will be fifth from the right in the new group of letters thus formed?
N
Understanding the HYDROMETER Word Transformation
The problem asks us to take the word HYDROMETER, apply a specific letter transformation, arrange the new letters alphabetically, and then find the letter that is fifth from the right end of this final sequence.
Step 1: Letter Transformation
We need to replace each letter in HYDROMETER with the letter that comes immediately before it in the English alphabet.
Let's list the letters of HYDROMETER and their preceding letters:
| Original Letter | Preceding Letter |
|---|---|
| H | G |
| Y | X |
| D | C |
| R | Q |
| O | N |
| M | L |
| E | D |
| T | S |
| E | D |
| R | Q |
So, the sequence of transformed letters is: G, X, C, Q, N, L, D, S, D, Q.
Step 2: Arranging Letters Alphabetically
Now, we arrange the transformed letters (G, X, C, Q, N, L, D, S, D, Q) in alphabetical order:
- C
- D
- D
- G
- L
- N
- Q
- Q
- S
- X
The alphabetized sequence is: C, D, D, G, L, N, Q, Q, S, X.
Step 3: Finding the Fifth Letter from the Right
We need to find the letter that is fifth from the right end of the alphabetized sequence (C, D, D, G, L, N, Q, Q, S, X). Let's count from the right:
- 1st from the right: X
- 2nd from the right: S
- 3rd from the right: Q
- 4th from the right: Q
- 5th from the right: N
Therefore, the letter that will be fifth from the right in the new group of letters is N.
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