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

It is currently 20 Oct 2014, 10:00

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

Does the integer k have at least three different positive

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23344
Followers: 3601

Kudos [?]: 28629 [0], given: 2806

Does the integer k have at least three different positive [#permalink] New post 09 Jul 2012, 03:51
Expert's post
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

77% (01:45) correct 23% (00:57) wrong based on 182 sessions
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23344
Followers: 3601

Kudos [?]: 28629 [0], given: 2806

Re: Does the integer k have at least three different positive [#permalink] New post 09 Jul 2012, 03:51
Expert's post
SOLUTION

Does the integer k have at least three different positive prime factors?

(1) k/15 is an integer --> since k is divisible by 3*5=15, then it's divisible by 3 and 5, hence k has at least those two prime factors, though it might have more (consider k=30). Not sufficient.

(2) k/10 is an integer --> since k is divisible by 2*5=10, then it's divisible by 2 and 5, hence k has at least those two prime factors, though it might have more (consider k=30). Not sufficient.

(1)+(2) At least 3 primes are factors of k: 2, 3, and 5. Sufficient.

Answer: C.
_________________

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

Senior Manager
Senior Manager
User avatar
Joined: 28 Mar 2012
Posts: 286
Concentration: Entrepreneurship
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 16

Kudos [?]: 172 [0], given: 23

GMAT ToolKit User
Re: Does the integer k have at least three different positive [#permalink] New post 09 Jul 2012, 04:44
Bunuel wrote:
Does the integer k have at least three different positive prime factors?

(1) k/15 is an integer.
(2) k/10 is an integer.

Hi,

For integer k to have atleast 3 different positive prime factors,
k = a.b.c, where a, b, c are prime numbers.

Using (1),
k/15 is an integer,
least value of k =15, which has two different prime factors 3 & 5. Insufficient.

Using (2),
k/10 is an integer,
least value of k =10 which has two different prime factors 2 & 5. Insufficient.

Using both,
least value of k =30 which has two different prime factors 2, 3 & 5. Sufficient.

Answer is (C)

Regards,
_________________

My posts: Solving Inequalities, Solving Simultaneous equations, Divisibility Rules

My story: 640 What a blunder!

Vocabulary resource: EdPrep

Facebook page: fb.com/EdPrep

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23344
Followers: 3601

Kudos [?]: 28629 [0], given: 2806

Re: Does the integer k have at least three different positive [#permalink] New post 13 Jul 2012, 02:53
Expert's post
SOLUTION

Does the integer k have at least three different positive prime factors?

(1) k/15 is an integer --> since k is divisible by 3*5=15, then it's divisible by 3 and 5, hence k has at least those two prime factors, though it might have more (consider k=30). Not sufficient.

(2) k/10 is an integer --> since k is divisible by 2*5=10, then it's divisible by 2 and 5, hence k has at least those two prime factors, though it might have more (consider k=30). Not sufficient.

(1)+(2) At least 3 primes are factors of k: 2, 3, and 5. Sufficient.

Answer: C.
_________________

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

Senior Manager
Senior Manager
avatar
Joined: 22 Nov 2010
Posts: 293
Location: India
GMAT 1: 670 Q49 V33
WE: Consulting (Telecommunications)
Followers: 5

Kudos [?]: 29 [0], given: 75

Re: Does the integer k have at least three different positive [#permalink] New post 16 Jul 2012, 23:46
If a divides b, then all the primes in a along with their powers are in b
_________________

YOU CAN, IF YOU THINK YOU CAN

Intern
Intern
avatar
Joined: 22 Oct 2013
Posts: 3
Followers: 0

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

Does the integer k... [#permalink] New post 14 Nov 2013, 14:45
This is in the official GMAT review book.

Does the integer k have at least three different positive prime factors?

1. k/15 is an integer.
2. k/10 is an integer.

The book says
[Reveal] Spoiler:
the answer is C
, but shouldn't
[Reveal] Spoiler:
the answer be E? Couldn't k = 0?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23344
Followers: 3601

Kudos [?]: 28629 [0], given: 2806

Re: Does the integer k... [#permalink] New post 14 Nov 2013, 14:49
Expert's post
jdiamond wrote:
This is in the official GMAT review book.

Does the integer k have at least three different positive prime factors?

1. k/15 is an integer.
2. k/10 is an integer.

The book says
[Reveal] Spoiler:
the answer is C
, but shouldn't
[Reveal] Spoiler:
the answer be E? Couldn't k = 0?


Merging similar topics. Please refer to the solutions above.

All OG13 questions are here: the-official-guide-quantitative-question-directory-143450.html
_________________

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

Intern
Intern
avatar
Joined: 22 Oct 2013
Posts: 3
Followers: 0

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

Re: Does the integer k... [#permalink] New post 14 Nov 2013, 15:08
Bunuel wrote:
jdiamond wrote:
This is in the official GMAT review book.

Does the integer k have at least three different positive prime factors?

1. k/15 is an integer.
2. k/10 is an integer.

The book says
[Reveal] Spoiler:
the answer is C
, but shouldn't
[Reveal] Spoiler:
the answer be E? Couldn't k = 0?


Merging similar topics. Please refer to the solutions above.


I didn't know this was here already. I don't think my issue with the question is answered in the solutions above.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23344
Followers: 3601

Kudos [?]: 28629 [0], given: 2806

Re: Does the integer k... [#permalink] New post 14 Nov 2013, 15:12
Expert's post
jdiamond wrote:
Bunuel wrote:
jdiamond wrote:
This is in the official GMAT review book.

Does the integer k have at least three different positive prime factors?

1. k/15 is an integer.
2. k/10 is an integer.

The book says
[Reveal] Spoiler:
the answer is C
, but shouldn't
[Reveal] Spoiler:
the answer be E? Couldn't k = 0?


Merging similar topics. Please refer to the solutions above.


I didn't know this was here already. I don't think my issue with the question is answered in the solutions above.


0 is a multiple of all integers except 0 itself. Thus if k=0 it still has at least three different positive prime factors.
_________________

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

Re: Does the integer k...   [#permalink] 14 Nov 2013, 15:12
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic If K is the least positive integer that is divisible by ever gmatgambler 2 05 Apr 2014, 04:40
1 Experts publish their posts in the topic If k is a positive integer, does k have more than 3 differen Galiya 4 30 Jun 2012, 07:22
2 Experts publish their posts in the topic Does the integer k have at least three different positive dzodzo85 6 27 Mar 2012, 01:57
2 Experts publish their posts in the topic Does the integer k have at least three different positive bandit 34 19 Apr 2009, 09:24
If the units digit of the three-digit positive integer k is NEWKID 2 06 Nov 2004, 09:29
Display posts from previous: Sort by

Does the integer k have at least three different positive

  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®.