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Letters of the word ‘ARRANGEMENT’ are first written in ascending order and then in descending order, and this process is continued. The (812)th letter of the above series is :
- a)A
- b)R
- c)E
- d)N
- e)T
Correct answer is option 'C'. Can you explain this answer?
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Letters of the word ‘ARRANGEMENT’ are first written in asc...
Problem Analysis:
In this problem, we are given a word "ARRANGEMENT" and we have to find the (812)th letter in the series that is formed by writing the letters of the word in ascending and then descending order repeatedly.
Solution:
To solve this problem, we will break it down into steps:
1. Determine the pattern of the series.
2. Calculate the number of letters in each repetition of the series.
3. Find the position of the (812)th letter in the series.
4. Identify the letter at that position.
Step 1: Determine the pattern of the series:
To find the pattern of the series, we need to write the letters of the word "ARRANGEMENT" in ascending and then descending order repeatedly.
Ascending order: A A E E G M N N R R R T
Descending order: T R R R N N M G E E A A
By observing the pattern, we can see that the series is formed by arranging the letters of the word in ascending order first, followed by descending order. This pattern continues infinitely.
Step 2: Calculate the number of letters in each repetition of the series:
To calculate the number of letters in each repetition of the series, we need to determine the length of the ascending and descending sequences.
Ascending sequence: A A E E G M N N R R R T (11 letters)
Descending sequence: T R R R N N M G E E A A (11 letters)
The total number of letters in each repetition of the series is 22.
Step 3: Find the position of the (812)th letter in the series:
To find the position of the (812)th letter in the series, we need to divide 812 by the number of letters in each repetition of the series and find the remainder.
812 ÷ 22 = 36 remainder 20
The (812)th letter is in the 36th repetition of the series and has a remainder of 20.
Step 4: Identify the letter at that position:
To identify the letter at the (812)th position, we need to count 20 letters from the beginning of the ascending sequence.
A A E E G M N N R R R T
The 20th letter is 'E'.
Therefore, the (812)th letter in the series is 'E'.
Hence, the correct answer is option 'C'.
In this problem, we are given a word "ARRANGEMENT" and we have to find the (812)th letter in the series that is formed by writing the letters of the word in ascending and then descending order repeatedly.
Solution:
To solve this problem, we will break it down into steps:
1. Determine the pattern of the series.
2. Calculate the number of letters in each repetition of the series.
3. Find the position of the (812)th letter in the series.
4. Identify the letter at that position.
Step 1: Determine the pattern of the series:
To find the pattern of the series, we need to write the letters of the word "ARRANGEMENT" in ascending and then descending order repeatedly.
Ascending order: A A E E G M N N R R R T
Descending order: T R R R N N M G E E A A
By observing the pattern, we can see that the series is formed by arranging the letters of the word in ascending order first, followed by descending order. This pattern continues infinitely.
Step 2: Calculate the number of letters in each repetition of the series:
To calculate the number of letters in each repetition of the series, we need to determine the length of the ascending and descending sequences.
Ascending sequence: A A E E G M N N R R R T (11 letters)
Descending sequence: T R R R N N M G E E A A (11 letters)
The total number of letters in each repetition of the series is 22.
Step 3: Find the position of the (812)th letter in the series:
To find the position of the (812)th letter in the series, we need to divide 812 by the number of letters in each repetition of the series and find the remainder.
812 ÷ 22 = 36 remainder 20
The (812)th letter is in the 36th repetition of the series and has a remainder of 20.
Step 4: Identify the letter at that position:
To identify the letter at the (812)th position, we need to count 20 letters from the beginning of the ascending sequence.
A A E E G M N N R R R T
The 20th letter is 'E'.
Therefore, the (812)th letter in the series is 'E'.
Hence, the correct answer is option 'C'.
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Letters of the word ‘ARRANGEMENT’ are first written in asc...
Solution: The word ‘ARRANGEMENT’ has 11 alphabets. Hence in the given series each alphabet will repeat after (22n - 1) terms, where n = 1,2,3......and so on. i.e. A will have the position 22n + 1 for n = 0, 1 , 2 , 3 ...... and so on.
The required term will also follow this pattern.
Therefore, to find the (812)th term of the series, find the remainder when 812 is divided by 22.
Remainder when 812 divided by 22 is,
The required term will also follow this pattern.
Therefore, to find the (812)th term of the series, find the remainder when 812 is divided by 22.
Remainder when 812 divided by 22 is,
Now, the 20th letter of the series is E.
Hence, E will be the (812) th letter of the series. Hence, option 3.
Hence, E will be the (812) th letter of the series. Hence, option 3.
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Letters of the word ‘ARRANGEMENT’ are first written in ascending order and then in descending order, and this process is continued. The (812)th letter of the above series is :a)Ab)Rc)Ed)Ne)TCorrect answer is option 'C'. Can you explain this answer?
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