GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Jun 2019, 01:02

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.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Intern
Intern
avatar
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

New post 31 Aug 2016, 22:16
1
2
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

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

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
Senior Manager
User avatar
S
Joined: 12 Sep 2017
Posts: 267
What is the sum of all 3 digit positive integers that can be formed  [#permalink]

Show Tags

New post 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.

If the answers were:

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

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

Show Tags

New post 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

Posted from my mobile device
GMAT Club Bot
Re: What is the sum of all 3 digit positive integers that can be formed   [#permalink] 20 Feb 2019, 23:55
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne