Find all School-related info fast with the new School-Specific MBA Forum

It is currently 12 Feb 2016, 08:19
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
User avatar
Joined: 23 Dec 2009
Posts: 49
Schools: HBS 2+2
WE 1: Consulting
WE 2: Investment Management
Followers: 0

Kudos [?]: 25 [0], given: 7

What is the sum of all 3 digit positive integers that can be formed us [#permalink] New post 30 Dec 2009, 02:29
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

61% (02:14) correct 39% (01:43) wrong based on 56 sessions
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

[Reveal] Spoiler:
First off, I'm not even sure if this is worded coherently. Does this mean 111, 588, and 811 are included in this set?

I figured it couldn't be "A", "B", "C", or "D" because they would be too small:

A: 158 is already > 126
B: 855 + 588 + 585 is already > 126
C: 855 + 885 + 585 + 588 + 558 + 811 + 818 is already > 126
D: ...
E: POE got me here.
[Reveal] Spoiler: OA

_________________

My GMAT quest...

...over!


Last edited by R2I4D on 30 Dec 2009, 03:19, edited 1 time in total.
1 KUDOS received
Manager
Manager
avatar
Joined: 09 May 2009
Posts: 202
Followers: 1

Kudos [?]: 166 [1] , given: 13

Re: What is the sum of all 3 digit positive integers that can be formed us [#permalink] New post 30 Dec 2009, 02:47
1
This post received
KUDOS
1
This post was
BOOKMARKED
there will 9 times 1 , 9 times 5 and nine times 8 at each place in a 3 digit no. with repetition

sum will be =100*9*(1+58) + 10*9*(1+5+8) + 1*9*(1+5+8)=13986

in order to know how it is 9 times

tot no. of ways =3*3*3=27
so in tot 27 words will be formed where each digit among 1,5,8 wil be repeated equal no. of times i.e 27/3=9
hence we have 9 , 1's ; 9 5's and 9 8's at each level
_________________

GMAT is not a game for losers , and the moment u decide to appear for it u are no more a loser........ITS A BRAIN GAME

Intern
Intern
User avatar
Joined: 23 Dec 2009
Posts: 49
Schools: HBS 2+2
WE 1: Consulting
WE 2: Investment Management
Followers: 0

Kudos [?]: 25 [0], given: 7

Re: What is the sum of all 3 digit positive integers that can be formed us [#permalink] New post 30 Dec 2009, 03:36
xcusemeplz2009 wrote:
there will 9 times 1 , 9 times 5 and nine times 8 at each place in a 3 digit no. with repetition

sum will be =100*9*(1+58) + 10*9*(1+5+8) + 1*9*(1+5+8)=13986

in order to know how it is 9 times

tot no. of ways =3*3*3=27
so in tot 27 words will be formed where each digit among 1,5,8 wil be repeated equal no. of times i.e 27/3=9
hence we have 9 , 1's ; 9 5's and 9 8's at each level


Wow. I have no idea what is happening here. Would you (or someone else) mind explaining a bit more...perhaps expounding on your method a little bit?

Perhaps, the same deal, with a two digit number using 1 and 2, with digits allowed to repeat?

[Answer: 11+12+21+22 = 66]

How can I use xcusemeplz2009's method to arrive at the same answer?
_________________

My GMAT quest...

...over!

2 KUDOS received
Manager
Manager
avatar
Joined: 09 May 2009
Posts: 202
Followers: 1

Kudos [?]: 166 [2] , given: 13

Re: What is the sum of all 3 digit positive integers that can be formed us [#permalink] New post 30 Dec 2009, 05:34
2
This post received
KUDOS
R2I4D wrote:
Wow. I have no idea what is happening here. Would you (or someone else) mind explaining a bit more...perhaps expounding on your method a little bit?

Perhaps, the same deal, with a two digit number using 1 and 2, with digits allowed to repeat?

[Answer: 11+12+21+22 = 66]

How can I use xcusemeplz2009's method to arrive at the same answer?


let me try again

let the no. be xyz
Place value of no will be 100x+10y+Z.............eqn 1

TOTAL NO OF WAYS IN WHICH WE CAN MAKE A NO. WITH GIVEN CONDITION IS 3*3*3=27( as digits are getting repeated)

now at unit place i.e Z if we fix 1 , then for y we have 3 options and for x we have 3 options , so total number where unit digit is one can be formed in 3*3=9 ways

similarly for other digits at unit place can be done in 9 ways

hence at unit place a digit is getting repeated 9 times

and in the same manner in tenths place repetion for all digits will be 9 each

now the task is to find the sum
sum of digits at z place is 9*1+9*5+9*8 , WHICH
IS SAME FOR Y AND X
for that we need to put all the options in eqn 1 format
i.e 100*9[1+5+8] + 10*9[1+5+8] + 9*[1+5+8]=13986

simple way is to remeber the quick formula to find out the repetition

find out tot no. ways in which the no. can be formed and divide it by the no. of digit , then mutiply this factor with the summation of all the dig and the place value

for second ex : 1,2

two dig no with repetn can be formewd in 2*2=4 ways , repetion factor=4/2 =2 ( tot no. of ways / tot no of dig)

sum=10(place value) * 2 (rep factor) *(1+2 summation of dig)+2*3=60+6=66
_________________

GMAT is not a game for losers , and the moment u decide to appear for it u are no more a loser........ITS A BRAIN GAME

Senior Manager
Senior Manager
User avatar
Joined: 22 Dec 2009
Posts: 362
Followers: 11

Kudos [?]: 293 [0], given: 47

GMAT ToolKit User
Re: What is the sum of all 3 digit positive integers that can be formed us [#permalink] New post 01 Jan 2010, 10:06
Pretty impressive formula used by xcusemeplz2009. +1 for that!

Nevertheless the question can be solved with POE as it is quite logical....

digits in scope = 1,5,8..
with this we can get highest 3 or 4 numbers - 888, 885, 881, 858.
Adding just these 4 numbers gives us = 3512
and we have 23 more numbers to be added... Hence the correct answer would be E of course!

Cheers!
JT
_________________

Cheers!
JT...........
If u like my post..... payback in Kudos!! :beer

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice|
|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|


~~Better Burn Out... Than Fade Away~~

1 KUDOS received
Manager
Manager
User avatar
Joined: 13 Apr 2015
Posts: 58
Concentration: General Management, Strategy
GMAT 1: 600 Q45 V28
GPA: 3.25
WE: Project Management (Energy and Utilities)
Followers: 1

Kudos [?]: 3 [1] , given: 325

CAT Tests
Re: What is the sum of all 3 digit positive integers that can be formed us [#permalink] New post 31 Oct 2015, 07:31
1
This post received
KUDOS
1
This post was
BOOKMARKED
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.
Re: What is the sum of all 3 digit positive integers that can be formed us   [#permalink] 31 Oct 2015, 07:31
    Similar topics Author Replies Last post
Similar
Topics:
16 Experts publish their posts in the topic How many four-digit positive integers can be formed by using gmihir 15 22 May 2012, 08:35
45 Experts publish their posts in the topic What is the sum of all 4-digit numbers that can be formed dimitri92 16 25 May 2010, 23:38
12 Experts publish their posts in the topic Find the sum of all 3-digit nos that can be formed by 1, 2 jusjmkol740 9 07 Jan 2010, 01:17
25 Experts publish their posts in the topic What is the sum of all 3 digit positive integers that can be formed sdrandom1 20 28 Jun 2009, 18:01
85 Experts publish their posts in the topic What is the sum of all 3 digit positive integers that can be asimov 19 29 Apr 2009, 00:06
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.