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

 It is currently 29 Aug 2016, 22:05

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

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

Hide Tags

Manager
Joined: 12 Feb 2012
Posts: 136
Followers: 1

Kudos [?]: 47 [0], given: 28

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

Show Tags

08 Apr 2012, 19:36
1
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

71% (01:59) correct 29% (01:08) wrong based on 74 sessions

HideShow timer Statistics

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.
VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1353
Followers: 17

Kudos [?]: 218 [1] , given: 10

Re: Divisibility , Cubic Power [#permalink]

Show Tags

08 Apr 2012, 22:51
1
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 !!

Math Expert
Joined: 02 Sep 2009
Posts: 34496
Followers: 6297

Kudos [?]: 79890 [1] , given: 10022

Re: If x^(1/3) is a positive integer, does x^(1/3) have more [#permalink]

Show Tags

09 Apr 2012, 00:58
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
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.

_________________
Director
Joined: 24 Aug 2009
Posts: 504
Schools: Harvard, Columbia, Stern, Booth, LSB,
Followers: 13

Kudos [?]: 623 [0], given: 241

Re: If x^(1/3) is a positive integer, does x^(1/3) have more [#permalink]

Show Tags

13 Sep 2012, 04:04
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

_________________

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

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11133
Followers: 511

Kudos [?]: 134 [1] , given: 0

Re: If x^(1/3) is a positive integer, does x^(1/3) have more [#permalink]

Show Tags

12 Jun 2016, 04:30
1
KUDOS
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.
_________________
Senior Manager
Joined: 02 Mar 2012
Posts: 369
Schools: Schulich '16
Followers: 3

Kudos [?]: 52 [0], given: 4

Re: If x^(1/3) is a positive integer, does x^(1/3) have more [#permalink]

Show Tags

12 Jun 2016, 08:10
A

1) x=125 .so x^1/3 =5 only 1&5 as factors.Suff

2)x^1/3 can be 25 or 5 which has more than 2 and only 2 factors.Not Suff
Director
Joined: 18 Oct 2014
Posts: 908
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
Followers: 74

Kudos [?]: 150 [0], given: 64

Re: If x^(1/3) is a positive integer, does x^(1/3) have more [#permalink]

Show Tags

13 Jun 2016, 09:26
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.

x^1/3 is prime or not?

(1) 64 < x < 216
64^1/3 < x^1/3 < 216 ^1/3
4<< x^1/3 <6

Since x^1/3 is an integer it will be 5 (prime). sufficient

(2) x is divisible by 5. Well it can be 5 or any multiple of 5. not sufficient.

_________________

I welcome critical analysis of my post!! That will help me reach 700+

Re: If x^(1/3) is a positive integer, does x^(1/3) have more   [#permalink] 13 Jun 2016, 09:26
Similar topics Replies Last post
Similar
Topics:
1 If n is a positive integer, does n have four or more distinct factors? 4 13 Jul 2016, 10:50
If A and B are positive integers > 1, does A have more unique prime 1 22 Apr 2016, 04:43
7 If n is a positive integer, does n have four or more distinct factors? 12 18 Mar 2015, 05:03
4 If k is a positive integer, does k have more than 3 differen 5 30 Jun 2012, 08:22
If z is a positive integer, does z have more than 2 positive 4 20 Jun 2011, 20:46
Display posts from previous: Sort by