Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 31 May 2012
Posts: 108

Re: What is the sum of all 3 digit positive integers that can be formed us
[#permalink]
Show Tags
04 Jan 2013, 07:43
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 formed us
[#permalink]
Show Tags
05 Jan 2013, 09:58
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
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 7128
City: Pune

What is the sum of all 3 digit positive integers that can be formed us
[#permalink]
Show Tags
05 Jan 2013, 10:40
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 = 13986. E
_________________
2020 MBA Applicants: Introduce Yourself Here!
MBA Video Series  Video answers to specific components and questions about MBA applications.
2020 MBA Deadlines, Essay Questions and Analysis of all top MBA programs



Manager
Joined: 26 Sep 2013
Posts: 184
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41

Re: What is the sum of all 3 digit positive integers that can be formed us
[#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: 58427

Re: What is the sum of all 3 digit positive integers that can be formed us
[#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.
_________________



Manager
Joined: 13 Apr 2015
Posts: 73
Concentration: General Management, Strategy
GPA: 3.25
WE: Project Management (Energy and Utilities)

Re: What is the sum of all 3 digit positive integers that can be formed us
[#permalink]
Show Tags
31 Oct 2015, 08:31
The Ans is E.
This can also be solved by using a formula
Sum of N numbers
With repetition = N ^ ( N  1 ) * Sum of the Numbers * 111..... N no. of times
With out repetition = ( N  1 ) ! * Sum of the Numbers * 111.... N no. of times.
Here repetition is allowed, therefore N is 3 ( No. of digits given ) and sum of No is 14.
3^2 * 14 * 111 = 13986.



Intern
Joined: 29 Oct 2015
Posts: 1

Re: What is the sum of all 3 digit positive integers that can be formed us
[#permalink]
Show Tags
27 Nov 2015, 00:06
Used POE, No need to solve the whole question to get an exact value Explanation:
since three digit numbers formed by 1, 5, 8 would be : Lets start with numbers starting with 8 : 888, 885, 881, 855, 851, 815, 811 sum of these numbers is greater than Options A , B , C , D Hence Ans: E.
Keep it simple ppl
Good luck!! Cheers



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15309
Location: United States (CA)

Re: What is the sum of all 3 digit positive integers that can be formed us
[#permalink]
Show Tags
28 Nov 2015, 20:45
Hi All, There's a great 'patternmatching' shortcut built into this question that can help you to avoid much of the 'math work' involved. We're told to use the digits 1, 5 and 8 to form every possible 3digit number (including those with duplicate digits) and then take the sum of those numbers. Since the digits can be repeated, we're dealing with the numbers that fall into the range of 111 to 888, inclusive. There are (3)(3)(3) = 27 total numbers and 1/3 of those numbers will begin with an 8. From THAT deduction, we know that the sum of those 9 numbers will be greater than (9)(800) = 7200. There's only one answer that fits that description... Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Manager
Joined: 17 Jun 2015
Posts: 195
GMAT 1: 540 Q39 V26 GMAT 2: 680 Q46 V37

Re: What is the sum of all 3 digit positive integers that can be formed us
[#permalink]
Show Tags
28 Dec 2015, 14:26
With 1 in the hundreds place, there are 9 numbers that could be created, since repetition is allowed. So 1 occurs 9 times in hundreds place = 900 Similarly it occurs 9 times in tens place = 90 and 9 times in ones place = 9 999 * 1 = 999 Similarly for 5 and 8 999 ( 1 + 5 + 8) = 999 * 14 = (1000  1) * 14 = 14,000  14 = 13,986
_________________
Fais de ta vie un rêve et d'un rêve une réalité



Manager
Joined: 06 Jun 2014
Posts: 85
Location: United States
Concentration: Finance, General Management
GPA: 3.47

Re: What is the sum of all 3 digit positive integers that can be formed us
[#permalink]
Show Tags
04 Jan 2016, 15:17
(1+5+8) * 9 = 126 (1+5+8) * 9 * 10 = 1260 (1+5+8) * 9 * 10 * 10 =12600
add 126+1260+12600= 13,986



Senior Manager
Joined: 23 Apr 2015
Posts: 284
Location: United States
Concentration: General Management, International Business
WE: Engineering (Consulting)

Re: What is the sum of all 3 digit positive integers that can be formed us
[#permalink]
Show Tags
23 Aug 2016, 20:52
R2I4D 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
I took a crude approach, the smallest number is 111 and largest is 888 and the number of integers are 3 * 3 * 3 = 27. the smallest is 111 and largest is 888, so the mean is around 500, so 500*27 = 13,500. E is the answer. +1 for kudos



Senior Manager
Joined: 23 Apr 2015
Posts: 284
Location: United States
Concentration: General Management, International Business
WE: Engineering (Consulting)

Re: What is the sum of all 3 digit positive integers that can be formed us
[#permalink]
Show Tags
24 Aug 2016, 19:51
sdrandom1 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 There are in total 3 * 3 * 3 = 27 numbers in these combinations. The smallest is 111 and largest is 888, so the avg is approx, 500. So the sum is approx 27 * 500 = 13,500 , close to E.



Intern
Joined: 29 May 2015
Posts: 10

Re: What is the sum of all 3 digit positive integers that can be formed us
[#permalink]
Show Tags
31 Aug 2016, 22:16
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.



Intern
Joined: 27 Jan 2019
Posts: 8

What is the sum of all 3 digit positive integers that can be formed us
[#permalink]
Show Tags
13 May 2019, 18:29
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 All these big formulas that people have used to solve this question are super impressive. However, it is much easier to answer this question using common sense and leveraging the answer choices. If you simply write out the possibilities of three digit integers that would begin with an eight, such as 888, 818, 851, 815, 885, 858 (not sure if I'm missing some here), you'll see that the sum of just the 8s is greater than ~4800. Logically, therefore, once you take into account all the combinations, the number will be much bigger than ~4,800. All but one answer choice remains; therefore, E is the correct answer.



Intern
Joined: 01 Sep 2016
Posts: 5

Re: What is the sum of all 3 digit positive integers that can be formed us
[#permalink]
Show Tags
19 Aug 2019, 22:59
Narenn wrote: 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 The solution given has a typo error. It’s written as 13896, whereas it should be 13986
_________________
Best Regards,
Abhishek Roy



Math Expert
Joined: 02 Sep 2009
Posts: 58427

Re: What is the sum of all 3 digit positive integers that can be formed us
[#permalink]
Show Tags
19 Aug 2019, 23:03
drroy wrote: Narenn wrote: 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 The solution given has a typo error. It’s written as 13896, whereas it should be 13986 _____________________ Fixed the typo. Thank you.
_________________




Re: What is the sum of all 3 digit positive integers that can be formed us
[#permalink]
19 Aug 2019, 23:03



Go to page
Previous
1 2
[ 36 posts ]



