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

It is currently 22 Aug 2014, 07:41

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

If k is the sum of the digits of integer m, and m=18n, where

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
3 KUDOS received
Intern
Intern
avatar
Joined: 20 Jun 2011
Posts: 46
Followers: 1

Kudos [?]: 12 [3] , given: 1

If k is the sum of the digits of integer m, and m=18n, where [#permalink] New post 23 Jul 2012, 09:59
3
This post received
KUDOS
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

48% (02:02) correct 52% (01:29) wrong based on 186 sessions
If k is the sum of the digits of integer m, and m=18n, where n is an integer, which of the following must be true?

A. The sum of the digits of m is 9
B. The sum of the digits of k is 9
C. m is a multiple of 2k
D. k is a multiple of 9
E. k is a multiple of 6
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Aug 2012, 22:22, edited 1 time in total.
Edited the question.
Intern
Intern
avatar
Joined: 21 Sep 2010
Posts: 6
Followers: 0

Kudos [?]: 4 [0], given: 9

Re: If k is the sum of the digits of integer m, and m=18n, where [#permalink] New post 23 Jul 2012, 11:48
Great question. Made me think for a while.

My answer is D.) "K is a multiple of 9".

We know that M is always divisible by 18 which means that M is always divisible by 9. This implies that the sum of the digits of M (also referred to as k) will ALWAYs be divisible by 9 (refer to the divisibility rules if you want confirmation).

I kept thinking 0 was a loophole until I realized that 0 is a multiple of ALL integers so in the case k=0 (occurs when n=0), k is still a multiple of 9. I also got stuck for a bit on answer choice E.) "K is a multiple of 6" until some plug-n-chug at n=1 disproved this answer.

I'd be very interested in seeing how other people solved this - please post if you used a different route of thinking.
Manager
Manager
avatar
Joined: 27 May 2012
Posts: 213
Followers: 0

Kudos [?]: 47 [0], given: 150

Re: If k is the sum of the digits of integer m, and m=18n, where [#permalink] New post 14 Aug 2012, 22:10
Club909 wrote:
Great question. Made me think for a while.

My answer is D.) "K is a multiple of 9".

We know that M is always divisible by 18 which means that M is always divisible by 9. This implies that the sum of the digits of M (also referred to as k) will ALWAYs be divisible by 9 (refer to the divisibility rules if you want confirmation).

I kept thinking 0 was a loophole until I realized that 0 is a multiple of ALL integers so in the case k=0 (occurs when n=0), k is still a multiple of 9. I also got stuck for a bit on answer choice E.) "K is a multiple of 6" until some plug-n-chug at n=1 disproved this answer.

I'd be very interested in seeing how other people solved this - please post if you used a different route of thinking.


D says that k has to be a multiple of 9
K = sum of the digits of M

so lets a couple of cases

we know m = 18 n

when n=0 m=0 so k =0 and k is a multiple of 9 , D is true

when n=1,2...6 m= 18, 36,....108 so k = 9 again K is a multiple of 9 , D is again true

when n = -1 or -2 or -6 then m = -18 or -36 or -108 then k = 7 or 3 or 7 ..but now K is not a multiple of 9 ??

so how can D always be true ??

Please note question does not mention that n is a positive integer or M is a positive integer .
if n is a negative integer as shown above then m will be negative and the sum of the digits of M will not always be 9 so please do explain
how D is always true ??
_________________

- Stne

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19048
Followers: 3369

Kudos [?]: 24519 [1] , given: 2680

Re: If k is the sum of the digits of integer m, and m=18n, where [#permalink] New post 14 Aug 2012, 22:26
1
This post received
KUDOS
Expert's post
stne wrote:
Club909 wrote:
Great question. Made me think for a while.

My answer is D.) "K is a multiple of 9".

We know that M is always divisible by 18 which means that M is always divisible by 9. This implies that the sum of the digits of M (also referred to as k) will ALWAYs be divisible by 9 (refer to the divisibility rules if you want confirmation).

I kept thinking 0 was a loophole until I realized that 0 is a multiple of ALL integers so in the case k=0 (occurs when n=0), k is still a multiple of 9. I also got stuck for a bit on answer choice E.) "K is a multiple of 6" until some plug-n-chug at n=1 disproved this answer.

I'd be very interested in seeing how other people solved this - please post if you used a different route of thinking.


D says that k has to be a multiple of 9
K = sum of the digits of M

so lets a couple of cases

we know m = 18 n

when n=0 m=0 so k =0 and k is a multiple of 9 , D is true

when n=1,2...6 m= 18, 36,....108 so k = 9 again K is a multiple of 9 , D is again true

when n = -1 or -2 or -6 then m = -18 or -36 or -108 then k = 7 or 3 or 7 ..but now K is not a multiple of 9 ??

so how can D always be true ??

Please note question does not mention that n is a positive integer or M is a positive integer .
if n is a negative integer as shown above then m will be negative and the sum of the digits of M will not always be 9 so please do explain
how D is always true ??


The sum of the digits of -18 is still 9 (1+8) not not 7 (-1+8).

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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. ,11 Mixed Questions, 12 Fresh Meat

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., 11 New DS set.


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

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 27 May 2012
Posts: 213
Followers: 0

Kudos [?]: 47 [0], given: 150

Re: If k is the sum of the digits of integer m, and m=18n, where [#permalink] New post 14 Aug 2012, 22:34
Bunuel wrote:
stne wrote:
Club909 wrote:
Great question. Made me think for a while.

My answer is D.) "K is a multiple of 9".

We know that M is always divisible by 18 which means that M is always divisible by 9. This implies that the sum of the digits of M (also referred to as k) will ALWAYs be divisible by 9 (refer to the divisibility rules if you want confirmation).

I kept thinking 0 was a loophole until I realized that 0 is a multiple of ALL integers so in the case k=0 (occurs when n=0), k is still a multiple of 9. I also got stuck for a bit on answer choice E.) "K is a multiple of 6" until some plug-n-chug at n=1 disproved this answer.

I'd be very interested in seeing how other people solved this - please post if you used a different route of thinking.


D says that k has to be a multiple of 9
K = sum of the digits of M

so lets a couple of cases

we know m = 18 n

when n=0 m=0 so k =0 and k is a multiple of 9 , D is true

when n=1,2...6 m= 18, 36,....108 so k = 9 again K is a multiple of 9 , D is again true

when n = -1 or -2 or -6 then m = -18 or -36 or -108 then k = 7 or 3 or 7 ..but now K is not a multiple of 9 ??

so how can D always be true ??

Please note question does not mention that n is a positive integer or M is a positive integer .
if n is a negative integer as shown above then m will be negative and the sum of the digits of M will not always be 9 so please do explain
how D is always true ??


The sum of the digits of -18 is still 9 (1+8) not not 7 (-1+8).

Hope it's clear.


Ok, if - 18 = 1+8 then D is always true , Got it
_________________

- Stne

Senior Manager
Senior Manager
User avatar
Joined: 23 Oct 2010
Posts: 384
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Followers: 11

Kudos [?]: 129 [0], given: 73

GMAT ToolKit User
Re: If k is the sum of the digits of integer m, and m=18n, where [#permalink] New post 15 Aug 2012, 10:12
m=18n means 18*n? when I saw 18n, I thought k=m=1+8+n=9+n and couldnt find any solution
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

1 KUDOS received
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 613
WE: Science (Education)
Followers: 68

Kudos [?]: 500 [1] , given: 43

GMAT Tests User
Re: If k is the sum of the digits of integer m, and m=18n, where [#permalink] New post 15 Aug 2012, 10:46
1
This post received
KUDOS
LalaB wrote:
m=18n means 18*n? when I saw 18n, I thought k=m=1+8+n=9+n and couldnt find any solution


It wasn't stated "the three-digit number 18n".
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Intern
Intern
avatar
Joined: 19 Feb 2012
Posts: 17
Followers: 0

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

GMAT ToolKit User
Re: If k is the sum of the digits of integer m, and m=18n, where [#permalink] New post 24 Nov 2012, 06:16
I think b is also correct

Image Posted from GMAT ToolKit
1 KUDOS received
Intern
Intern
avatar
Joined: 29 Dec 2012
Posts: 3
Concentration: Finance, International Business
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 1 [1] , given: 18

Re: If k is the sum of the digits of integer m, and m=18n, where [#permalink] New post 27 Jan 2013, 10:48
1
This post received
KUDOS
B is incorrect. Try m=18 * 11 and you will find that the sum of digits is not 9.

-Abhishek
Senior Manager
Senior Manager
avatar
Joined: 16 Feb 2012
Posts: 259
Concentration: Finance, Economics
Followers: 4

Kudos [?]: 53 [0], given: 106

GMAT ToolKit User
Re: If k is the sum of the digits of integer m, and m=18n, where [#permalink] New post 12 Feb 2013, 08:28
Could someone explain in which cases k is not a multiple of 6. Thank you!
_________________

Kudos if you like the post!

Failing to plan is planning to fail.

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19048
Followers: 3369

Kudos [?]: 24519 [0], given: 2680

Re: If k is the sum of the digits of integer m, and m=18n, where [#permalink] New post 12 Feb 2013, 08:33
Expert's post
Stiv wrote:
If k is the sum of the digits of integer m, and m=18n, where n is an integer, which of the following must be true?

A. The sum of the digits of m is 9
B. The sum of the digits of k is 9
C. m is a multiple of 2k
D. k is a multiple of 9
E. k is a multiple of 6

Could someone explain in which cases k is not a multiple of 6. Thank you!



m=18 --> k=1+8=9 --> 9 is NOT a multiple of 6.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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. ,11 Mixed Questions, 12 Fresh Meat

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., 11 New DS set.


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

Get the best GMAT Prep Resources with GMAT Club Premium Membership

SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1627
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 11

Kudos [?]: 152 [0], given: 254

GMAT ToolKit User
Re: If k is the sum of the digits of integer m, and m=18n, where [#permalink] New post 12 Nov 2013, 16:23
superpus07 wrote:
If k is the sum of the digits of integer m, and m=18n, where n is an integer, which of the following must be true?

A. The sum of the digits of m is 9
B. The sum of the digits of k is 9
C. m is a multiple of 2k
D. k is a multiple of 9
E. k is a multiple of 6


I could figure out an easy solution for this one. Anyone have any idea how to solve this efficiently?
Will throw some nice Kudos out there!

Cheers
J :)
Intern
Intern
avatar
Joined: 24 May 2012
Posts: 6
Concentration: Technology, Entrepreneurship
Followers: 0

Kudos [?]: 0 [0], given: 13

Re: If k is the sum of the digits of integer m, and m=18n, where [#permalink] New post 07 Dec 2013, 14:26
Can someone post an example of a case when C is not true?
2 KUDOS received
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 15 Jun 2012
Posts: 1006
Location: United States
Followers: 117

Kudos [?]: 1166 [2] , given: 118

Premium Member
Re: If k is the sum of the digits of integer m, and m=18n, where [#permalink] New post 08 Dec 2013, 00:57
2
This post received
KUDOS
lajulajay wrote:
Can someone post an example of a case when C is not true?


Hello lajulajay

Let try n = 11
==> m = 18*11 = 198
==> k = 1 + 9 + 8 = 18
==> 2k = 36

But 198 / 36 = 5.5 ==> C is not always correct.

Hope it helps.
_________________

Please +1 KUDO if my post helps. Thank you.

"Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong."

Chris Bangle - Former BMV Chief of Design.

Re: If k is the sum of the digits of integer m, and m=18n, where   [#permalink] 08 Dec 2013, 00:57
    Similar topics Author Replies Last post
Similar
Topics:
7 Experts publish their posts in the topic If 5400mn = k^4, where m, n, and k are positive integers banksy 7 13 Feb 2011, 13:20
PR and MN are 2-digit positive integers, where P, R, M, and arjtryarjtry 6 01 Aug 2008, 02:14
If K=m*n^5, where n is an integer and m=4^n. Is K>0? (1) arjtryarjtry 5 31 Jul 2008, 19:35
Experts publish their posts in the topic Q) K is an integer. If the sum of each digit numbers of this pretttyune 3 26 Nov 2007, 04:51
How many digits does m^3 have, where m is an integer? (1) m freetheking 12 02 Aug 2006, 21:16
Display posts from previous: Sort by

If k is the sum of the digits of integer m, and m=18n, where

  Question banks Downloads My Bookmarks Reviews Important topics  


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®.