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09 Feb 2021, 09:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
47% (02:22) correct
53%
(02:41)
wrong
based on 100
sessions
History
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Time
Result
Not Attempted Yet
The 120 permutations of MAHES are arranged in dictionary order, as if each were an ordinary five-letter word. The last letter of the 86th word in the list is
(A) A
(B) H
(C) S
(D) E
(E) M
(A) A
(B) H
(C) S
(D) E
(E) M
10 Feb 2021, 04:54
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Let us divide the 120 permutations into 5 categories: words beginning with M, A, H, E and S respectively.
In each category, we have 4! = 24 words (number of permutations of the remaining letters, except the first letter).
The first 24 words begin with A
The next 24 words begin with E
The next 24 words begin with H
Thus, we have now accounted for the first 72 words of the dictionary. If we count the next 24 words beginning with M, we exceed our required word number of 86. Therefore, the 86th word begins with M.
Now, the 24 words beginning with M can be further sub-categorized into 4 categories of words - those beginning with A, E, H and S - each containing 3! = 6 words.
The first 6 words (words 73 to 78) begin with MA.
The next 6 words (words 79 to 84) begin with ME.
Word 85, thus, has to be MHAES.
Word 86 has to be MHASE.
Correct answer: (D)
In each category, we have 4! = 24 words (number of permutations of the remaining letters, except the first letter).
The first 24 words begin with A
The next 24 words begin with E
The next 24 words begin with H
Thus, we have now accounted for the first 72 words of the dictionary. If we count the next 24 words beginning with M, we exceed our required word number of 86. Therefore, the 86th word begins with M.
Now, the 24 words beginning with M can be further sub-categorized into 4 categories of words - those beginning with A, E, H and S - each containing 3! = 6 words.
The first 6 words (words 73 to 78) begin with MA.
The next 6 words (words 79 to 84) begin with ME.
Word 85, thus, has to be MHAES.
Word 86 has to be MHASE.
Correct answer: (D)
10 Feb 2021, 05:20
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AEHMS
With A as the first word, total words = 4*3*2*1 = 24
Similarly, with E as the first word, total words = 4*3*2*1 = 24
Similarly, with H as the first word, total words = 4*3*2*1 = 24
That makes a total of 72
Now, let's come to M as the first letter and:
i) A as the second letter, total words = 3*2*1 = 6 (that makes a total of 78)
ii) E as the second letter, total words = 3*2*1 = 6 (that makes a total of 84)
With H as the second letter:
85th word is MHAES
86th word is MHASE
So, 'E' is the last letter of the 86th word.
With A as the first word, total words = 4*3*2*1 = 24
Similarly, with E as the first word, total words = 4*3*2*1 = 24
Similarly, with H as the first word, total words = 4*3*2*1 = 24
That makes a total of 72
Now, let's come to M as the first letter and:
i) A as the second letter, total words = 3*2*1 = 6 (that makes a total of 78)
ii) E as the second letter, total words = 3*2*1 = 6 (that makes a total of 84)
With H as the second letter:
85th word is MHAES
86th word is MHASE
So, 'E' is the last letter of the 86th word.
