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Number properties?

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by jk2010 » Fri Jan 07, 2011 12:28 pm
This question is a bit off format, so I apologize in advance. I just took my GMAT and there was a problem that read something to the effect of:

Set S consists of 4 positive integers, all of which are made up of 1,2,3,and 4 such as 2341 or 3412. The number 3341 was not in the set. What was the sum of Set S?

I don't recall the numbers, but the units digit was either 5 or 0, and the numbers ranged from 16,660 to 200,000.

Sorry for the scant details, but I assume there is a basic strategy for tackling this sort of problem.

Thanks.
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by anshumishra » Fri Jan 07, 2011 2:47 pm
jk2010 wrote:This question is a bit off format, so I apologize in advance. I just took my GMAT and there was a problem that read something to the effect of:

Set S consists of 4 positive integers, all of which are made up of 1,2,3,and 4 such as 2341 or 3412. The number 3341 was not in the set. What was the sum of Set S?

I don't recall the numbers, but the units digit was either 5 or 0, and the numbers ranged from 16,660 to 200,000.

Sorry for the scant details, but I assume there is a basic strategy for tackling this sort of problem.

Thanks.

Numbers -> 1,2,3,4

No. of ways to arrange them so that none of them repeat = 4! = 24
The set contains these 24 numbers.
Now if you write these 24 numbers, all the 4 digits (1,2,3,4) appear 6 times on each digit place. So, sum of the unit/ten/hundred/thousand digits =
6(1+2+3+4) = 60

So the total sum = 60(1000+100+10+1) = 60*1111 = 66660
Thanks
Anshu

(Every mistake is a lesson learned )
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