Find all School-related info fast with the new School-Specific MBA Forum
Learn more about the recent changes... close

It is currently 24 May 2013, 18:44
Customize  |  Hide

Search
Register
New posts
Unanswered

The sum of all the digits of the positive integer q is equal

  Question banks Downloads My Bookmarks Reviews  
  Oldest Best Reply
Search for:
 
Print view
First unread post
Author Message
TAGS:
1 KUDOS received
Director
Director
Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
Posts: 558
Location: United Kingdom
Concentration: International Business, Strategy
GMAT Date: 06-22-2012
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 8

Kudos [?]: 63 [1] , given: 212

GMAT Tests User
The sum of all the digits of the positive integer q is equal [#permalink] New post 21 Jan 2012, 16:02
1
This post received
KUDOS
00:00

Question Stats:

65% (03:21) correct 34% (02:52) wrong based on 5 sessions
The sum of all the digits of the positive integer q is equal to the three-digit number x13. If q = 10^n – 49, what is the value of n?

(A) 24
(B) 25
(C) 26
(D) 27
(E) 28
[Reveal] Spoiler: OA

_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610 :-(

2 KUDOS received
GMAT Club team member
User avatar
Joined: 02 Sep 2009
Posts: 11611
Followers: 1801

Kudos [?]: 9597 [2] , given: 829

GMAT Tests User CAT Tests
Top Member of the Month
Re: Value of n [#permalink] New post 21 Jan 2012, 16:18
2
This post received
KUDOS
enigma123 wrote:
The sum of all the digits of the positive integer q is equal to the three-digit number x13. If q = 10^n – 49, what is the value of n?
(A) 24
(B) 25
(C) 26
(D) 27
(E) 28

Any idea how to approach this problem?


10^n has n+1 digits: 1 and n zeros. For example: 10^2=100 --> 3 digits: 1 and 2 zeros;

10^n-49 will have n digits: n-2 9's and 51 in the and. For example: 10^4-49=10,000-49=9,951 --> 4 digits: 4-2=two 9's and 51 in the end;

We are told that the sum of all the digits of 10^n-49 is equal to the three-digit number x13 --> 9(n-2)+5+1=x13 --> 9n-12=x13 --> 9n=x25 --> x25 is divisible by 9 --> the sum of its digits must be divisible by 9 --> x=2 --> 9n=225 --> n=25.

Answer: B.

Hope it's clear.
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

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. NEW!!!

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. NEW!!!


What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates

Director
Director
Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
Posts: 558
Location: United Kingdom
Concentration: International Business, Strategy
GMAT Date: 06-22-2012
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 8

Kudos [?]: 63 [0], given: 212

GMAT Tests User
Re: The sum of all the digits of the positive integer q is equal [#permalink] New post 21 Jan 2012, 17:03
Sorry Bunuel - Struggling to understand how you got to 10^n-49 will have n digits: n-2 9's and 51 in the end. For example: 10^4=10,000-51=9,949 --> 4 digits: 4-2=two 9's and 49 in the end;
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610 :-(

1 KUDOS received
GMAT Club team member
User avatar
Joined: 02 Sep 2009
Posts: 11611
Followers: 1801

Kudos [?]: 9597 [1] , given: 829

GMAT Tests User CAT Tests
Top Member of the Month
Re: The sum of all the digits of the positive integer q is equal [#permalink] New post 21 Jan 2012, 17:14
1
This post received
KUDOS
enigma123 wrote:
Sorry Bunuel - Struggling to understand how you got to 10^n-49 will have n digits: n-2 9's and 51 in the end. For example: 10^4=10,000-51=9,949 --> 4 digits: 4-2=two 9's and 49 in the end;


10^n-49 will have n digits: n-2 9's and 51 in the and. For example: 10^4-49=10,000-49=9,951 --> 4 digits: 4-2=two 9's and 51 in the end;

Or maybe this will help:
10^n has n+1 digits: 1 and n zeros;
10^n-49 has n digits, so one less digit than 10^n. In the end it'll have 51 (the same way 1,000-49=951) and the rest of the digits, so n-2 digits, will be 9's.

Hope it's clear.
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

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. NEW!!!

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. NEW!!!


What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates

Manager
Manager
Joined: 12 Nov 2011
Posts: 145
Followers: 0

Kudos [?]: 1 [0], given: 24

GMAT Tests User
Re: The sum of all the digits of the positive integer q is equal [#permalink] New post 22 Jan 2012, 08:42
My way
after pluging n=2, n=3, n=4 you see that digits go according to the pattern "9(k times)51" where k=n-2
so you left with => 9*k+5+1=x13, n=k+2, find n, try numbers and solve it easy
Director
Director
Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
Posts: 558
Location: United Kingdom
Concentration: International Business, Strategy
GMAT Date: 06-22-2012
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 8

Kudos [?]: 63 [0], given: 212

GMAT Tests User
Re: The sum of all the digits of the positive integer q is equal [#permalink] New post 24 Jan 2012, 18:20
Bunuel - again struggling. Can you please explain how did you get to this ?

We are told that the sum of all the digits of 10^n-49 is equal to the three-digit number x13
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610 :-(

Director
Director
Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
Posts: 558
Location: United Kingdom
Concentration: International Business, Strategy
GMAT Date: 06-22-2012
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 8

Kudos [?]: 63 [0], given: 212

GMAT Tests User
Re: The sum of all the digits of the positive integer q is equal [#permalink] New post 24 Jan 2012, 18:20
I mean the solution after the line above.
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610 :-(

Director
Director
Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
Posts: 558
Location: United Kingdom
Concentration: International Business, Strategy
GMAT Date: 06-22-2012
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 8

Kudos [?]: 63 [0], given: 212

GMAT Tests User
Re: The sum of all the digits of the positive integer q is equal [#permalink] New post 24 Jan 2012, 18:22
Got it thanks. Sorry its bit late in the night at my end.
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610 :-(

Senior Manager
Senior Manager
Joined: 24 Aug 2009
Posts: 283
Schools: Harvard, Columbia, Stern, Booth, LSB,
Followers: 2

Kudos [?]: 138 [0], given: 218

Re: The sum of all the digits of the positive integer q is equal [#permalink] New post 17 Aug 2012, 23:24
Again the best solution by Bunuel.
I think the question should be written as clear as possible to avoid any confusion.

The stem of the question should be {The sum of all the digits of the positive integer q is equal to the three-digit number which is x13.....} rather than {The sum of all the digits of the positive integer q is equal to the three-digit number x13.}
(A) 24
(B) 25
(C) 26
(D) 27
(E) 28
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth -Game Theory

Intern
Intern
Joined: 20 Jun 2011
Posts: 36
Followers: 0

Kudos [?]: 3 [0], given: 1

Re: Value of n [#permalink] New post 14 Sep 2012, 07:56
Bunuel wrote:

10^n has n+1 digits: 1 and n zeros. For example: 10^2=100 --> 3 digits: 1 and 2 zeros;

10^n-49 will have n digits: n-2 9's and 51 in the and. For example: 10^4-49=10,000-49=9,951 --> 4 digits: 4-2=two 9's and 51 in the end;

We are told that the sum of all the digits of 10^n-49 is equal to the three-digit number x13 --> 9(n-2)+5+1=x13 --> 9n-12=x13 --> 9n=x25 --> x25 is divisible by 9 --> the sum of its digits must be divisible by 9 --> x=2 --> 9n=225 --> n=25.

Answer: B.

Hope it's clear.


I'm just wondering about this approach: I tried to find a pattern.

n= 2 --> sum of digits = 6
n= 3 --> sum of digits = 15
n= 4 --> sum of digits = 24
n= 5 --> sum of digits = 33
(an increase of 9 for every n)

So for every odd n we get an odd units digit in the sum. And since x13 ends with an odd (3) number, I eliminated ans. choices A, C and E.

As for B and D - I was guessing/hoping that the units digit would stay on 3 for multiples of 5. So I picked ans. choice B).

But after thinking about it. I think I got lucky. So I'm wondering if there is something/similar that relates to this approach that yields a correct answer every time?

Thanks.
1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 468
Followers: 12

Kudos [?]: 75 [1] , given: 11

GMAT ToolKit User GMAT Tests User
Re: The sum of all the digits of the positive integer q is equal [#permalink] New post 21 Dec 2012, 07:29
1
This post received
KUDOS
enigma123 wrote:
The sum of all the digits of the positive integer q is equal to the three-digit number x13. If q = 10^n – 49, what is the value of n?

(A) 24
(B) 25
(C) 26
(D) 27
(E) 28


10^2 - 49 = 51
10^3 - 49 = 951
10^4 - 49 = 9951

The sum of digits 5 and 1 is 5 + 1 = 6. In order to get x13, we need to add a units digit 7 to 6.

(A) 10^24 gives 22 9s = 9*22 = units digit 8
(B) 10^25 gives 23 9s = 9*23 = units digit 7

Answer: B
Re: The sum of all the digits of the positive integer q is equal   [#permalink] 21 Dec 2012, 07:29
    Similar topics Author Replies Last post
Similar
Topics:
 New posts There are positive integers P, Q, R; are they all equal? (by csperber 5 05 Dec 2003, 15:13
New posts What is the sum of all 3-digit positive integers that leave thearch 6 04 Jun 2005, 09:06
New posts What is the sum of all two digit positive integers when the sparky 3 12 Jun 2005, 14:57
New posts There are positive integers P, Q, and R. Are they all equal? gk3.14 6 31 Aug 2006, 20:48
Popular new posts 10 EXPERTS_POSTS_IN_THIS_TOPIC What is the sum of all 3 digit positive integers that can be asimov 15 29 Apr 2009, 01:06
Display posts from previous: Sort by

The sum of all the digits of the positive integer q is equal

  Question banks Downloads My Bookmarks Reviews  
Print view
First unread post

Moderators: Bunuel, VeritasPrepKarishma, IanStewart

Search for:


GMAT Club MBA Forum Home| About| Privacy Policy| 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®.

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com