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# What is the sum of all 3 digit positive integers that can be formed

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Intern
Joined: 29 May 2015
Posts: 10
Re: What is the sum of all 3 digit positive integers that can be formed us  [#permalink]

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31 Aug 2016, 22:16
1
2
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:46) correct 34% (02:09) wrong based on 364 sessions

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What is the sum of all 3 digit positive integers that can be formed using the digits 1, 5, and 8, if the digits are allowed to repeat within a number?

A. 126
B. 1386
C. 3108
D. 308
E. 13986

Before solving, I knew that the number will be big but did not know how big.
As I did not know a fancy way of solving this, I just tried to find the number if the digits are NOT allowed to repeat.
Then it would be,

158
185
518
581
815
851

And just by rough estimation, it looked like it will be in 3000 range. As the question stem says digits ARE allowed to repeat, meaning,
there should be more than 3000. The only answer more than 3000 was E.
Senior Manager
Joined: 12 Sep 2017
Posts: 267
What is the sum of all 3 digit positive integers that can be formed  [#permalink]

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20 Feb 2019, 19:53
vityakim wrote:
What is the sum of all 3 digit positive integers that can be formed using the digits 1, 5, and 8, if the digits are allowed to repeat within a number?

A. 126
B. 1386
C. 3108
D. 308
E. 13986

Hello!

Could someone please explain to me the following statement?

"are allowed to repeat within a number?"

It's a bit confusing for me.

Btw, the question was very easy because of the range of the answers but, could someone please provide the correct approach for this kind of questions?

Ex.

A. 9255
B. 10576
C. 11369
D. 13980
E. 13986

Intern
Joined: 20 Feb 2019
Posts: 2
Re: What is the sum of all 3 digit positive integers that can be formed  [#permalink]

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20 Feb 2019, 23:55
Repeating a digit within a number means arrangements such as 155, 558, 888 etc are valid.

Since repeating is allowed, total number of permutations- 3x3x3=27. Now for a fixed units digit, say 5, the number of permutations will be 3x3=9. This will be the same for UD 1 and UD 8.

This means if we imagine a good ol' addition stack then all the UDs will add up to 9x(1+5+8)=126. Imagine putting 6 and carrying 12 forward. Repeat the same process for Tens Digits. It's the same 9x(1+5+8) story for all three of UDs, TDs and HDs. Don't forget to add the 12 carried forward. Then do the same for HDs and u get 13986

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Re: What is the sum of all 3 digit positive integers that can be formed   [#permalink] 20 Feb 2019, 23:55
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