Author 
Message 
TAGS:

Hide Tags

VP
Joined: 08 Apr 2009
Posts: 1212
Concentration: General Management, Strategy
Schools: Duke (Fuqua)  Class of 2012

What is the sum of all 3 digit positive integers that can be [#permalink]
Show Tags
29 Apr 2009, 01:06
5
This post received KUDOS
36
This post was BOOKMARKED
Question Stats:
70% (01:13) correct 30% (01:19) wrong based on 891 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.



Intern
Joined: 26 Apr 2009
Posts: 6

Re: sum of 3 digit #s [#permalink]
Show Tags
29 Apr 2009, 06:24
9
This post received KUDOS
8
This post was BOOKMARKED
E
summing units (1+5+8)*9 + tens (1+5+8)*9*10 + hundreds (1+5+8)*9*100 =
= 126+1,260+12,600 = 13,986



VP
Joined: 08 Apr 2009
Posts: 1212
Concentration: General Management, Strategy
Schools: Duke (Fuqua)  Class of 2012

Re: sum of 3 digit #s [#permalink]
Show Tags
29 Apr 2009, 13:26
hi aismirnov, can you elaborated on your explanation a bit. I'm a bit weak with these types of problems. for example, what did you use tens (1+5+8)*9*10, etc.
tia



Intern
Joined: 26 Apr 2009
Posts: 6

Re: sum of 3 digit #s [#permalink]
Show Tags
30 Apr 2009, 00:24
19
This post received KUDOS
12
This post was BOOKMARKED
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?
Imagine, we have got all these possible numbers written down  there are in total 3^3 numbers (each digit can be either 1 or 5 or 8)
there are 3*3 options for having a number XY1 there are 3*3 options for having a number XY5 there are 3*3 options for having a number XY8
there are 3*3 options for having a number X1Z there are 3*3 options for having a number X5Z there are 3*3 options for having a number X8Z
there are 3*3 options for having a number 1YZ there are 3*3 options for having a number 5YZ there are 3*3 options for having a number 8YZ
we can sum units, tens and hundreds independently: summing units gives (1+5+8)*3*3 summing tens gives (1+5+8)*10*3*3 summing hundreds gives (1+5+8)*100*3*3



Manager
Joined: 11 Aug 2008
Posts: 135

Re: sum of 3 digit #s [#permalink]
Show Tags
14 Oct 2009, 18:47
6
This post received KUDOS
I don't have your specific method but by POE I still can have E. for 8xy alone we have 888,881,885,818,855,851,858,815,811. The total of them is larger than 7200 so there is only option E left



Manager
Joined: 14 Apr 2010
Posts: 199

Re: sum of 3 digit #s [#permalink]
Show Tags
09 Aug 2010, 21:33
this is how i approached 888 588 188 158 518 118 558 These are the number that can have 8 as the units digit. here, 8(7) = 56 so units dig is 6 similarly, for 5 as the units dig  5(7) = 35 so units dig is 5 for 1 as the units dig  1(7) = 7 as the unit dig. therfore, in the sum of these dig, the units dig will be 6+5+7 = 8 Please tell me where i am wrong



Manager
Joined: 27 Jul 2010
Posts: 175
Location: Prague
Schools: University of Economics Prague

Re: sum of 3 digit #s [#permalink]
Show Tags
02 Feb 2011, 03:15
3
This post received KUDOS
2
This post was BOOKMARKED
I sowe really good formula for solving this problem in some notes downloaded from this forum. I just cannot find it, so I appologize to the author. The formula says: Repetition allowed: SUM of digits * (n^n1)*(11111 ...number composed of n 1digits)
Repetition NOT allowed: SUM of digits * (n1)!*(11111 ...number composed of n 1digits) Here we have 3 digits. n is 3. Sum of digits 1+5+8=14 Repetition allowed: 14*(3^2)*111=13986 Repetition not allowed: 14*2*111=3108
_________________
You want somethin', go get it. Period!



Math Expert
Joined: 02 Sep 2009
Posts: 44654

Re: sum of 3 digit #s [#permalink]
Show Tags
02 Feb 2011, 03:37
5
This post received KUDOS
Expert's post
27
This post was BOOKMARKED
craky wrote: I sowe really good formula for solving this problem in some notes downloaded from this forum. I just cannot find it, so I appologize to the author. The formula says: Repetition allowed: SUM of digits * (n^n1)*(11111 ...number composed of n 1digits)
Repetition NOT allowed: SUM of digits * (n1)!*(11111 ...number composed of n 1digits) Here we have 3 digits. n is 3. Sum of digits 1+5+8=14 Repetition allowed: 14*(3^2)*111=13986 Repetition not allowed: 14*2*111=3108 It should be: 1. Sum of all the numbers which can be formed by using the \(n\) digits without repetition is: \((n1)!*(sum \ of \ the \ digits)*(111... \ n \ times)\). 2. Sum of all the numbers which can be formed by using the \(n\) digits ( repetition being allowed) is: \(n^{n1}*(sum \ of \ the \ digits)*(111... \ n \ times)\). Similar questions: nicequestionandagoodwaytosolve103523.htmlcansomeonehelp94836.htmlsumofall3digitnoswith88864.htmlpermutation88357.html
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 13 Aug 2012
Posts: 444
Concentration: Marketing, Finance
GPA: 3.23

What is the sum of all 3 digit positive integers that can be [#permalink]
Show Tags
20 Dec 2012, 04:15
1
This post received KUDOS
iwillwin wrote: What is the sum of all 3 digit positive numbers 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 Here is a formula to know the sum of possible arrangements when a digit is not allowed to repeat:\((n1)!*sumofdigits*111 = (31)!*(1+5+8)*111=28*111=3108\) But we know that digits are allowed to repeat. Thus, sum is much greater than 3108.Answer: E
_________________
Impossible is nothing to God.



Intern
Joined: 02 Nov 2012
Posts: 32

Re: What is the sum of all 3 digit positive integers that can be [#permalink]
Show Tags
04 Jan 2013, 06:50
I approach this particular problem without the formulae. Can somebody please help me if this is correct > If you know that the numbers are allowed to repeat then the possible numbers are 3*3*3 = 27 (instead of 3*2*1 when repetition is not allowed), then you know that there will be 9 ones, 9 fives, 9 eights. So for the first position you can have the 9+45+72 = 12600, then all the answer choices will fall except for E. If you calculate further you get 12600 + 01260 + 00126 = 13,986. Bunuel, Karishma or someone else can you please confirm if this is correct?



Manager
Joined: 31 May 2012
Posts: 150

Re: What is the sum of all 3 digit positive integers that can be [#permalink]
Show Tags
04 Jan 2013, 07:43
7
This post received KUDOS
asimov 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 One quickest way to answer this question !! As we are using digits 1,5, 8 and digits are allowed to repeat. Each of the unit, tenth and hundredth digit can be used by each of three digits. So, Total possible numbers with these digits=3 X 3 X 3 =27. First, As we have 27 three digit number, Sum will be for sure more than 2700.. Eliminate options A,B,D Second, If you imagine numbers with the given digits 1,5,8. We have numbers like 888,885,855,858,851. Sum is for sure more than 4000. Eliminate option C. You are left with answer E.  consider giving a +kudo if this helps



Intern
Joined: 11 Sep 2012
Posts: 7

Re: What is the sum of all 3 digit positive integers that can be [#permalink]
Show Tags
05 Jan 2013, 09:58
1
This post received KUDOS
1, 5 and 8 are allowed to be used 9 times as hundreds, tenths and units digit.
So you can line up:
9x100 9x 10 9x 1 9x500 9x 50 9x 5 9x800 9x 80 9x 8
When lining these up, you should quickly realize that it's bigger than 10.000 and pick your answer without going further.



MBA Section Director
Status: Back to work...
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 5101
Location: India
City: Pune
GPA: 3.4
WE: Business Development (Manufacturing)

Re: What is the sum of all 3 digit positive integers that can be [#permalink]
Show Tags
05 Jan 2013, 10:40
5
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
asimov 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 Answer to this question is easier to guess than to calculate. e.g. if we take 8 at hundreds place we would get at least 9 nos. So 800 * 9 = 7200 which surpasses every option but E. Thru conventional method (1+5+8)9 = 126 (1+5+8)9*10=1260 (1+5+8)9*100=12600 126 + 1260 + 12600 = 13896. E
_________________
Chances of Getting Admitted After an Interview [Data Crunch]
Must Read Forum Topics Before You Kick Off Your MBA Application
New GMAT Club Decision Tracker  Real Time Decision Updates



Manager
Joined: 26 Sep 2013
Posts: 204
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41

Re: sum of 3 digit #s [#permalink]
Show Tags
01 Oct 2013, 18:44
aismirnov 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?
Imagine, we have got all these possible numbers written down  there are in total 3^3 numbers (each digit can be either 1 or 5 or 8)
there are 3*3 options for having a number XY1 there are 3*3 options for having a number XY5 there are 3*3 options for having a number XY8
there are 3*3 options for having a number X1Z there are 3*3 options for having a number X5Z there are 3*3 options for having a number X8Z
there are 3*3 options for having a number 1YZ there are 3*3 options for having a number 5YZ there are 3*3 options for having a number 8YZ
we can sum units, tens and hundreds independently: summing units gives (1+5+8)*3*3 summing tens gives (1+5+8)*10*3*3 summing hundreds gives (1+5+8)*100*3*3 How did you know how to do this? I mean, how did you learn? I have 4 weeks to go until my GMAT and I haven't gotten any better at these. I have no idea how to even begin approaching these problems, and none of these formulas make any sense to me.



Math Expert
Joined: 02 Sep 2009
Posts: 44654

Re: sum of 3 digit #s [#permalink]
Show Tags
02 Oct 2013, 03:24
AccipiterQ wrote: aismirnov 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?
Imagine, we have got all these possible numbers written down  there are in total 3^3 numbers (each digit can be either 1 or 5 or 8)
there are 3*3 options for having a number XY1 there are 3*3 options for having a number XY5 there are 3*3 options for having a number XY8
there are 3*3 options for having a number X1Z there are 3*3 options for having a number X5Z there are 3*3 options for having a number X8Z
there are 3*3 options for having a number 1YZ there are 3*3 options for having a number 5YZ there are 3*3 options for having a number 8YZ
we can sum units, tens and hundreds independently: summing units gives (1+5+8)*3*3 summing tens gives (1+5+8)*10*3*3 summing hundreds gives (1+5+8)*100*3*3 How did you know how to do this? I mean, how did you learn? I have 4 weeks to go until my GMAT and I haven't gotten any better at these. I have no idea how to even begin approaching these problems, and none of these formulas make any sense to me. Direct formulas are here: whatisthesumofall3digitpositiveintegersthatcanbe78143.html#p862674 Please ask if anything there is unclear. Similar questions to practice: findthesumofallthefourdigitnumbersformedusingthe103523.htmlfindthesumofallthefourdigitnumberswhichareformed88357.htmlfindthesumofall3digitnosthatcanbeformedby88864.htmlifthethreeuniquepositivedigitsabandcarearranged143836.htmlwhatisthesumofall3digitpositiveintegersthatcanbe78143.htmlwhatisthesumofall4digitnumbersthatcanbeformed94836.htmlthesumofthedigitsof64279whatisthe141460.htmlthereare24differentfourdigitintegersthancanbe141891.htmltheadditionproblemaboveshowsfourofthe24differentin104166.htmlHope this helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



NonHuman User
Joined: 09 Sep 2013
Posts: 6645

Re: What is the sum of all 3 digit positive integers that can be [#permalink]
Show Tags
16 Nov 2017, 09:20
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: What is the sum of all 3 digit positive integers that can be
[#permalink]
16 Nov 2017, 09:20






