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# N is a 3-digit positive integer that composed of 1, 2, and 3

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Current Student
Joined: 11 May 2008
Posts: 551
N is a 3-digit positive integer that composed of 1, 2, and 3 [#permalink]

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28 Jul 2008, 02:56
N is a 3-digit positive integer that composed of 1, 2, and 3 without repetition. What is the sum of all such possible numbers?
A. 666
B. 726
C. 999
D. 1,221
E. 1,332

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Manager
Joined: 18 Aug 2006
Posts: 57
Location: Houston TX

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28 Jul 2008, 03:11
E.
There are 6 such numbers: 123+132+213+231+312+321=1,332
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haveaniceday

Manager
Joined: 15 Jul 2008
Posts: 205

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28 Jul 2008, 03:15
1332.

Since only 3 digit numbers are there, and that too without rep, i just wrote all of them and added.

123+132+231+213+312+321=1332.

o/w it would be an interesting problem. I would rely on guess work. Here is my take on how i would go about it.

u will have 2 numbers starting with 1. it will give u atleast 100+100.
u " " 2 " " " 2. it will give u atleast 200+200.
"do" 3. it will give u atleast 300+300.

total would give u atleast 1200. there are two numbers greater than 1200. so go for the next level, 10s place with the largest option.
with 1, u will have 30+20 atleast.. that itself puts u above 1250. so u can directly go to e.

I am sure, the gurus out here will be able to suggest better approach though
Senior Manager
Joined: 19 Mar 2008
Posts: 344

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28 Jul 2008, 09:06
1
arjtryarjtry wrote:
N is a 3-digit positive integer that composed of 1, 2, and 3 without repetition. What is the sum of all such possible numbers?
A. 666
B. 726
C. 999
D. 1,221
E. 1,332

E

For each digit:
possible number are 1, 2,3 and each will appear twice:
123
132
213
231
312
321

If you see the sum of each column is 1+1+2+2+3+3 = 12
so ans is
12+120+1200= 1332
Senior Manager
Joined: 06 Apr 2008
Posts: 393

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28 Jul 2008, 09:09
arjtryarjtry wrote:
N is a 3-digit positive integer that composed of 1, 2, and 3 without repetition. What is the sum of all such possible numbers?
A. 666
B. 726
C. 999
D. 1,221
E. 1,332

E) 123 + 132 + 213 + 231 + 312 + 321 = 1332

Faster calc. can be Sum of units digit = 12, Sum of tens digit = 12 and sum of hundreds digit = 12 which makes it 1332
Current Student
Joined: 28 Dec 2004
Posts: 3288
Location: New York City
Schools: Wharton'11 HBS'12

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28 Jul 2008, 09:47
arjtryarjtry wrote:
N is a 3-digit positive integer that composed of 1, 2, and 3 without repetition. What is the sum of all such possible numbers?
A. 666
B. 726
C. 999
D. 1,221
E. 1,332

whenever i see a symetric problem like this..

i just focus on 1 digit as the sum of the that digit would 10 times that for 10s, 100 times for hundreds and so on..

123
132
231
213
312
321
just focus on the unit digit.. 3+2+1+3+2+1 i.e 3*2 + 2*2 + 2*1=12

1200+120+12
1332
Current Student
Joined: 11 May 2008
Posts: 551

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29 Jul 2008, 10:15
fresinha... good tip... i think there is a prob similar to this somewhere here with the heading GMATPREP

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Re: 3digit positive integer   [#permalink] 29 Jul 2008, 10:15
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# N is a 3-digit positive integer that composed of 1, 2, and 3

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