MBA Spotlight – The Biggest MBA Fair is June 13-14
close
It is currently 30 May 2023, 05:15
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
New comers' posts

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel

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

29 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
   1   2 
User avatar
umeshpatil
Manager
Manager
Joined: 31 May 2012
Posts: 103
Re: What is the sum of all 3 digit positive integers that can be formed us [#permalink] New post  04 Jan 2013, 07:43
9
Kudos
1
Bookmarks
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 :lol:

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. :lol:

You are left with answer E.

----------------
consider giving a +kudo if this helps :-D
User avatar
L
Narenn
MBA Section Director
Joined: 22 Feb 2012
Affiliations: GMAT Club
Posts: 8469
GMAT ToolKit User
What is the sum of all 3 digit positive integers that can be formed us [#permalink] New post  05 Jan 2013, 10:40
5
Kudos
4
Bookmarks
Expert Reply
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
_________________
Register for MBA Spotlight | Meet with 25+ top business schools on June 13-14

Follow us on YouTube | Instagram | Twitter | Facebook
Signature Read More
avatar
AccipiterQ
Manager
Manager
Joined: 26 Sep 2013
Posts: 159
Concentration: Finance, Economics
Schools: HBS '16 (D) Sloan '16 (D) Carroll '16 (WA$) Boston U '16 (A$) Northeastern '16 (A)
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] New post  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.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 88688
CAT Tests Forum Quiz Mode Top Member of the Month
Re: What is the sum of all 3 digit positive integers that can be formed us [#permalink] New post  02 Oct 2013, 03:24
1
Kudos
4
Bookmarks
Expert Reply
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: what-is-the-sum-of-all-3-digit-positive-integers-that-can-be-78143.html#p862674 Please ask if anything there is unclear.

Similar questions to practice:
find-the-sum-of-all-the-four-digit-numbers-formed-using-the-103523.html
find-the-sum-of-all-the-four-digit-numbers-which-are-formed-88357.html
find-the-sum-of-all-3-digit-nos-that-can-be-formed-by-88864.html
if-the-three-unique-positive-digits-a-b-and-c-are-arranged-143836.html
what-is-the-sum-of-all-3-digit-positive-integers-that-can-be-78143.html
what-is-the-sum-of-all-4-digit-numbers-that-can-be-formed-94836.html
the-sum-of-the-digits-of-64-279-what-is-the-141460.html
there-are-24-different-four-digit-integers-than-can-be-141891.html
the-addition-problem-above-shows-four-of-the-24-different-in-104166.html

Hope this helps.
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
User avatar
goldfinchmonster
Manager
Manager
Joined: 13 Apr 2015
Posts: 61
Concentration: General Management, Strategy
Schools: Jenkins FT'18 (S) Desautels '18 Iowa State '18 DeGroote (II) UConn FT "18 Alberta'18 Haskayne(Calgary)
GMAT 1: 620 Q47 V28
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] New post  31 Oct 2015, 08:31
1
Kudos
9
Bookmarks
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.
avatar
mohitmohan23
Intern
Intern
Joined: 29 Oct 2015
Posts: 1
Re: What is the sum of all 3 digit positive integers that can be formed us [#permalink] New post  27 Nov 2015, 00:06
3
Kudos
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
User avatar
L
EMPOWERgmatRichC
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21481
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: What is the sum of all 3 digit positive integers that can be formed us [#permalink] New post  28 Nov 2015, 20:45
6
Kudos
Expert Reply
Hi All,

There's a great 'pattern-matching' 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 3-digit 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:
Show Spoiler
E


GMAT assassins aren't born, they're made,
Rich
_________________
EMPOWERgmat.com
The Course Used By GMAT Club Moderators To Earn 750+
Try it for FREE Today!

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Signature Read More
User avatar
L
dabaobao
Director
Director
Joined: 24 Oct 2016
Posts: 598
GMAT 1: 670 Q46 V36
GMAT 2: 690 Q47 V38
GMAT 3: 690 Q48 V37
GMAT 4: 710 Q49 V38 (Online)
Re: What is the sum of all 3 digit positive integers that can be formed us [#permalink] New post  15 Nov 2019, 19:05
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



Method 1: Sum Each Column of Digits



We need positive integers having 3 digits.

S = __ __ __

We can make 3*3*3 = 27 such positive integers since we can fill in each of the 3 spaces in 3 ways. Now imagine writing these 27 numbers one below the other to add.

158
185
...
...
x 27 combinations

When we add them, noticing the symmetry we know that there will be 9 1's in units digits, 9 5's and 9 8's. So units digits will add up to (1+5+8)*9.

Similarly, tens digits will add up (1+5+8)*9*10.
Similarly, hundreds digits will add up (1+5+8)*9*100

Adding all of them:
(1+5+8)*9 + (1+5+8)*9*10 + (1+5+8)*9*100 = (1+5+8) * 9 * (1+10+100) = 14 * 9 * 111 = 13,986


Method 2: Direct Formula



Sum of all n digit numbers formed by n non-zero digits with repetition being allowed is:

n^(n−1)∗(sum of the digits)∗(111... n times)

9 * 14 * 111 = 13,986

Answer: E
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6911
Location: Canada
Top Member of the Month
What is the sum of all 3 digit positive integers that can be formed us [#permalink] New post  04 Sep 2022, 07:57
Expert Reply
Top Contributor
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


Let's first calculate how many 3-digit numbers can be created using only the digits 1, 5 and 8.
There are 3 ways to choose a hundreds digit.
There are 3 ways to choose a tens digit.
There are 3 ways to choose a ones digit.
So, the total number of ways to create a three digit number = (3)(3)(3) = 27

Now let's focus on the hundreds digits of our 27 numbers.
9 (aka 1/3) of the 27 numbers will have hundreds digit 1. 9 x 100 = 900
9 (aka 1/3) of the 27 numbers will have hundreds digit 5. 9 x 500 = 4500
9 (aka 1/3) of the 27 numbers will have hundreds digit 8. 9 x 800 = 7200
900 + 4500 + 7200 = 12,600

So, if we ignore the tens and ones digits, the sum of our 27 numbers is already 12,600, which means the TOTAL sum must be greater than 12,600

Answer: E
_________________
Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing - Learn more
Signature Read More
GMAT Club Bot
gmatclubot
What is the sum of all 3 digit positive integers that can be formed us [#permalink]
04 Sep 2022, 07:57
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
   1   2 
Moderators:
Bunuel
Math Expert
88688 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3151 posts

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions