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

It is currently 18 Sep 2014, 23:55

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 x^(1/3) is a positive integer, does x^(1/3) have more

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 12 Feb 2012
Posts: 107
Followers: 1

Kudos [?]: 10 [0], given: 28

If x^(1/3) is a positive integer, does x^(1/3) have more [#permalink] New post 08 Apr 2012, 18:36
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

63% (01:47) correct 38% (01:10) wrong based on 27 sessions
If x^(1/3) is a positive integer, does x^(1/3) have more than two distinct integer factors?

(1) 64 < x < 216
(2) x is divisible by 5.

Cannot Find an OA: My Solution

[Reveal] Spoiler:
1) 64^(1/3)=4 , 125^(1/3)=5, and 216^(1/3)=6. Since x^(1/3) is an integer, x must equal 5. 5 is a prime number and only has two factors 1 and 5. So the answer is NO. Hence sufficient.

2) X=5k. Well 1000=5*200. x^(1/3)=1000^(1/3)=10 , which has 1,2,5,10 as its factors. So the answer the question is YES.
But we can also pick x=125=5*25. x^(1/3)=125^(1/3)=5, which has only two factors: 1 and 5. Hence the answer is NO. Hence INSUFF.
1 KUDOS received
VP
VP
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1365
Followers: 11

Kudos [?]: 140 [1] , given: 10

GMAT Tests User
Re: Divisibility , Cubic Power [#permalink] New post 08 Apr 2012, 21:51
1
This post received
KUDOS
b. x can be 125 or 125^3
thus x ^ (1/3) = 5 or 125, factors 1,5 or 1,5,25,125 so on.

hence Insufficient.

A it is.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23471
Followers: 3499

Kudos [?]: 26397 [1] , given: 2710

Re: If x^(1/3) is a positive integer, does x^(1/3) have more [#permalink] New post 08 Apr 2012, 23:58
1
This post received
KUDOS
Expert's post
If \sqrt[3]{x} is a positive integer, does \sqrt[3]{x} have more than two distinct integer factors?

(1) 64 < x < 216 --> take the cube root: 4<\sqrt[3]{x}<6 --> since given that \sqrt[3]{x}=integer then: \sqrt[3]{x}=5. 5 has only 2 distinct positive factors: 1 and 5. Sufficient.

(2) x is divisible by 5 --> if \sqrt[3]{x}=5 the answer is NO but if \sqrt[3]{x}=10 the answer is YES. Not sufficient.

Answer: A.
_________________

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

Director
Director
avatar
Joined: 24 Aug 2009
Posts: 509
Schools: Harvard, Columbia, Stern, Booth, LSB,
Followers: 9

Kudos [?]: 373 [0], given: 241

Re: If x^(1/3) is a positive integer, does x^(1/3) have more [#permalink] New post 13 Sep 2012, 03:04
alphabeta1234 wrote:
If x^(1/3) is a positive integer, does x^(1/3) have more than two distinct integer factors?

(1) 64 < x < 216
(2) x is divisible by 5.

Cannot Find an OA: My Solution

[Reveal] Spoiler:
1) 64^(1/3)=4 , 125^(1/3)=5, and 216^(1/3)=6. Since x^(1/3) is an integer, x must equal 5. 5 is a prime number and only has two factors 1 and 5. So the answer is NO. Hence sufficient.

2) X=5k. Well 1000=5*200. x^(1/3)=1000^(1/3)=10 , which has 1,2,5,10 as its factors. So the answer the question is YES.
But we can also pick x=125=5*25. x^(1/3)=125^(1/3)=5, which has only two factors: 1 and 5. Hence the answer is NO. Hence INSUFF.



Another way to look at the question.
Basically question says Is x^(1/3) a prime number, if x^(1/3) is a positive integer?
(1) x=5, which is a prime. -----> Sufficient
(2) x=5k, where is a positive integer -----> x= 5,10....----->Insufficient

Answer A
_________________

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

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Re: If x^(1/3) is a positive integer, does x^(1/3) have more   [#permalink] 13 Sep 2012, 03:04
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic If A and B are positive integers, does A have fewer factors LM 3 24 Oct 2012, 04:04
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
If z is a positive integer, does z have more than 2 positive guygmat 4 20 Jun 2011, 19:46
If x and y are none negative integer, x*y=? (1) 7^x=13^y (2) arjtryarjtry 1 25 Jul 2008, 02:48
If n is an integer and n= 2x3x5x7x11x13 77k Then which of neemo 6 27 Jun 2006, 15:09
Display posts from previous: Sort by

If x^(1/3) is a positive integer, does x^(1/3) have more

  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®.