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# Using the letters A, M, O, S, and U, we can form five-letter "words".

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Math Expert
Joined: 02 Sep 2009
Posts: 58434
Using the letters A, M, O, S, and U, we can form five-letter "words".  [#permalink]

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19 Mar 2019, 00:12
00:00

Difficulty:

55% (hard)

Question Stats:

58% (02:13) correct 42% (02:11) wrong based on 45 sessions

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Using the letters A, M, O, S, and U, we can form five-letter "words". If these "words" are arranged in alphabetical order, then the "word" USAMO occupies position

(A) 112
(B) 113
(C) 114
(D) 115
(E) 116

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Re: Using the letters A, M, O, S, and U, we can form five-letter "words".  [#permalink]

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19 Mar 2019, 00:32
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1
1
Hi I will try to answer this,
Correct me if I'm wrong

5! = 120 rankings
arrange alphabetically

A**** = 1-24
M**** = 25-48
O**** = 49-72
S**** = 73-96
U**** = 97-120

Range 97-120

4!/4 = 6

The ranking as follows

UA*** = 97-102
UM*** = 103-108
UO*** = 109-114
US*** = 115-120

and since AMO follows the alphabetical order, it should be the first list on the US*** word list
USAMO should be Number 115

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Re: Using the letters A, M, O, S, and U, we can form five-letter "words".  [#permalink]

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19 Mar 2019, 04:29
1
Bunuel wrote:
Using the letters A, M, O, S, and U, we can form five-letter "words". If these "words" are arranged in alphabetical order, then the "word" USAMO occupies position

(A) 112
(B) 113
(C) 114
(D) 115
(E) 116

total ways to arrange AMOSU = 5!= 120 WAYS
also for each starting alphabet we have total 120/5 = 24 ways each or say 4 position each for every string of letter ...
so until letter S we would have occupied 96 positions
for rest 24 positions ; from 97-114 = 18 would be occupied in series until we reach US..
so US series will start from 115 position
IMO D
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Re: Using the letters A, M, O, S, and U, we can form five-letter "words".  [#permalink]

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15 Sep 2019, 15:10
The total number of arrangements = 5! = 120
Options tell you that you are looking at the last few orders.
Last Arrangement will be : USOMA
List from 120th Position:
USOMA - 120
USOAM - 119
USMOA - 118
USMAO - 117
USAOM - 116
USAMO - 115
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Using the letters A, M, O, S, and U, we can form five-letter "words".  [#permalink]

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15 Sep 2019, 15:44
Total number of arrangements of AMOSU = 5! = 120. Scanning through the options (112 to 116), I quickly realize that US*** set should be the last set of arrangement.

The number of arrangements in US*** set = 1*1*3*2*1 = 6, spanning from #115 to #120. Just as US AMO is at the beginning of this last set, so it certainly occupies position no 115.

+1 kudo if you like this solution
Using the letters A, M, O, S, and U, we can form five-letter "words".   [#permalink] 15 Sep 2019, 15:44
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