Question

The position(s) of how many letters will remain unchanged if each letter in the word GRACEFUL is arranged in the English alphabetical order?

• A. Two
• B. None
• C. One
• D. Three

Answer 1

Answer:

B. None

Understanding Alphabetical Rearrangement Problems

These types of problems test your ability to systematically rearrange letters and compare them to the original position. The key is to perform the rearrangement accurately and then compare each letter's new position with its original one.

Steps for Solving:

1. Identify the given word: GRACEFUL

2. Determine the number of letters: The word GRACEFUL has 8 letters.

3. Arrange the letters in English alphabetical order:

   • Original Word: G R A C E F U L

   • Alphabetical Order: A C E F G L R U

4. Compare the original positions with the new positions:

   • Original: G R A C E F U L

   • Alphabetical: A C E F G L R U

   • Let's align them to compare:

   • G (1st) vs A (1st) - Changed

   • R (2nd) vs C (2nd) - Changed

   • A (3rd) vs E (3rd) - Changed

   • C (4th) vs F (4th) - Changed

   • E (5th) vs G (5th) - Changed

   • F (6th) vs L (6th) - Changed

   • U (7th) vs R (7th) - Changed

   • L (8th) vs U (8th) - Changed

5. Count the letters that remain in the same position: In this case, after rearranging the letters of GRACEFUL alphabetically (ACEFG LRU), none of the letters are in their original positions.