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

It is currently 04 Jul 2015, 01:24

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

For the positive integers a, b, and k, a^k||b means that a^k

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 02 Dec 2012
Posts: 178
Followers: 3

Kudos [?]: 828 [0], given: 0

For the positive integers a, b, and k, a^k||b means that a^k [#permalink] New post 12 Dec 2012, 02:59
7
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

72% (02:19) correct 28% (01:32) wrong based on 650 sessions
For the positive integers a, b, and k, a^k||b means that a^k is a divisor of b, but a^(k + 1) is not a divisor of b. If k is a positive integer and 2^k||72, then k is equal to

(A) 2
(B) 3
(C) 4
(D) 8
(E) 18
[Reveal] Spoiler: OA
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28272
Followers: 4469

Kudos [?]: 45143 [0], given: 6645

Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink] New post 12 Dec 2012, 03:02
Expert's post
3
This post was
BOOKMARKED
Walkabout wrote:
For the positive integers a, b, and k, a^k||b means that a^k is a divisor of b, but a^(k + 1) is not a divisor of b. If k is a positive integer and 2^k||72, then k is equal to

(A) 2
(B) 3
(C) 4
(D) 8
(E) 18


\(72=2^3*3^2\), so we have that 2^3 is a divisor of 72 and 2^4 is not. Thus 2^3||72, hence k=3.

Answer: B.
_________________

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

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
User avatar
Joined: 24 Apr 2012
Posts: 48
Followers: 0

Kudos [?]: 17 [0], given: 1

Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink] New post 14 Dec 2012, 02:20
Ans:

72= 2^3x3^2, since 2^3 is a divisor of 72 k can be 3. Also 2^4=(2^(k+1)) is not a divisor of 72 , therefore the answer is (B).
_________________

www.mnemoniceducation.com

TURN ON YOUR MINDS!!!

2 KUDOS received
Intern
Intern
avatar
Joined: 20 Aug 2012
Posts: 4
Followers: 0

Kudos [?]: 2 [2] , given: 4

Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink] New post 14 Dec 2012, 22:44
2
This post received
KUDOS
Initially looking to the problem one may try to plugin the numbers one by one. Here, 2^2=4 is a divisor of 72 and 2^3=8 is also a divisor of 72. But, we have to choose only one answer.
72=2x2x2x3x3=2^3 *3^2 and it is given that 72/2^k = integer. Here, we can equate 2^3=2^k and hence k=3. But, in fact 2^2 is also a divisor of 72 hence 2 could also be the answer. But, since it is additionally given that k+1 is not a divisor i.e. 2 in this case does not satisfy the condition because 2+1=3 and 2^3 is a divisior of 72. where as 3 satisfies the condition i.e. 3+1= 4 turning into 2^4 which is not a divisor of 72. This is how only one answer choice is left which is equal to 3 = answer choice B.
Intern
Intern
avatar
Joined: 26 May 2012
Posts: 21
Concentration: Marketing, Technology
GMAT Date: 09-17-2012
Followers: 1

Kudos [?]: 4 [0], given: 7

Reviews Badge
Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink] New post 19 Dec 2012, 06:15
2^k has to be a factor of 72.

Factors of 72: 3^2 x 2^3

Hence, k = 3.

Answer B.
1 KUDOS received
Intern
Intern
User avatar
Joined: 18 May 2013
Posts: 7
Location: Germany
GMAT Date: 09-27-2013
Followers: 0

Kudos [?]: 8 [1] , given: 55

GMAT ToolKit User
Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink] New post 25 Jul 2013, 07:30
1
This post received
KUDOS
1
This post was
BOOKMARKED
Prime factorization is also helpful to solve this problem. For ME it´s faster..

Probably it helps someone.
Attachments

PS 110 - prime factorization.jpg
PS 110 - prime factorization.jpg [ 20.75 KiB | Viewed 6069 times ]

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 5364
Followers: 310

Kudos [?]: 60 [0], given: 0

Premium Member
Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink] New post 11 Sep 2014, 01:40
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

1 KUDOS received
Manager
Manager
avatar
Joined: 07 Apr 2014
Posts: 147
Followers: 1

Kudos [?]: 11 [1] , given: 81

Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink] New post 11 Sep 2014, 10:29
1
This post received
KUDOS
Walkabout wrote:
For the positive integers a, b, and k, a^k||b means that a^k is a divisor of b, but a^(k + 1) is not a divisor of b. If k is a positive integer and 2^k||72, then k is equal to

(A) 2
(B) 3
(C) 4
(D) 8
(E) 18



72 = 2*2*2*3*3

72/ 2^k = int ; 72/2^k+1 not integer

if k= 2 then divisible ,k=3 then also ..
if K=3 then divisible , k=4 then not..

Answer =B
Senior Manager
Senior Manager
User avatar
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 400
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Followers: 1

Kudos [?]: 54 [0], given: 146

Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink] New post 02 Mar 2015, 01:35
If we say that 2^k is a divisor of 72 could we also do this to solve the problem?

Do the prime factorization of 72: 2^3 * 3^3, and then create the following equation:

2^k * 3^3 = 2^3 * 3^3, so k = 3?

Then we are assuming that k is 72, but 72 is still a divisor of 72. So, could we also do that?

As I see it, it is just a more visual way to say what everyone said above. Right...?
Re: For the positive integers a, b, and k, a^k||b means that a^k   [#permalink] 02 Mar 2015, 01:35
    Similar topics Author Replies Last post
Similar
Topics:
5 If P = k^3 – k, where k and P are positive integers, and k is given b manpreetsingh86 4 19 Nov 2014, 01:00
11 Experts publish their posts in the topic When the positive integer k is divided by the positive integ joaomario 6 12 Aug 2014, 04:00
5 Experts publish their posts in the topic If a, b, k, and m are positive integers, is a^k factor of b KocharRohit 5 06 Nov 2009, 22:12
The average (arithmetic mean) of the 5 positive integers k, vivek123 3 04 Mar 2006, 11:34
Display posts from previous: Sort by

For the positive integers a, b, and k, a^k||b means that a^k

  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®.