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27 Aug 2020, 22:45
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C
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Difficulty:
75%
(hard)
Question Stats:
55% (02:17) correct
45%
(02:19)
wrong
based on 132
sessions
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If all the words that can be formed from the letters of the word GARNE are taken and arranged in alphabetical order, then the rank of the word RANGE is?
A.101
B.100
C.102
D.78
E.99
A.101
B.100
C.102
D.78
E.99
28 Aug 2020, 00:54
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Given word: GRANE.
Alphabetical order: A,E,G,N,R
Keeping A as the first alphabet, total number of combinations: A*4*3*2=24
Similarly, for rest of the 3 alphabets: E, G, & N = 24*3 = 72
Total combination possible with A,E,G,N as the first alphabet: 24+72 =96
Now,Now to identify the rank of RANGE=
R as the first alphabet & A is the second alphabet, total number of worlds possible= R*A*3*2*1 = 6
Therefore: Range should come as =96+6 = 102 word. (since N is the last alphabet, when R is locked as first alphabet of the word).
I am not sure, if there is any simple way to get this math. please suggest.
Alphabetical order: A,E,G,N,R
Keeping A as the first alphabet, total number of combinations: A*4*3*2=24
Similarly, for rest of the 3 alphabets: E, G, & N = 24*3 = 72
Total combination possible with A,E,G,N as the first alphabet: 24+72 =96
Now,Now to identify the rank of RANGE=
R as the first alphabet & A is the second alphabet, total number of worlds possible= R*A*3*2*1 = 6
Therefore: Range should come as =96+6 = 102 word. (since N is the last alphabet, when R is locked as first alphabet of the word).
I am not sure, if there is any simple way to get this math. please suggest.
28 Aug 2020, 06:21
Kudos
Bookmarks
The five letters are different, so there are 5! = 120 'words' we can make in total. Of these, 1/5 will start with R, so 24 words start with R. That's the last letter alphabetically, so the last 24 words in our list begin with R, or the 97th through 120th ranked words.
Of those 24 words, exactly 1/4 of them, or 6 of them, will have an 'A' in the second position. A is the first letter alphabetically, so these six words will come first in our alphabetical ranking of the words beginning with R. So they'll occupy the 97th through 102nd positions in our list. Finally, of the six words you can make with E, G, N, the word "NGE" is last in alphabetical order, so RANGE must be the 102nd word overall.
Of those 24 words, exactly 1/4 of them, or 6 of them, will have an 'A' in the second position. A is the first letter alphabetically, so these six words will come first in our alphabetical ranking of the words beginning with R. So they'll occupy the 97th through 102nd positions in our list. Finally, of the six words you can make with E, G, N, the word "NGE" is last in alphabetical order, so RANGE must be the 102nd word overall.
