It is currently 20 Sep 2017, 04:24

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

It is known that cuberoot (r) is a positive integer

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Senior Manager
Senior Manager
avatar
Joined: 10 Apr 2012
Posts: 277

Kudos [?]: 1110 [0], given: 325

Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
GMAT ToolKit User Premium Member
It is known that cuberoot (r) is a positive integer [#permalink]

Show Tags

New post 21 Mar 2013, 01:09
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

42% (01:25) correct 58% (01:13) wrong based on 72 sessions

HideShow timer Statistics

It is known that \(\sqrt[3]{r}\) is a positive integer. Is \(\sqrt[3]{r}\) a prime number?

(1) All the factors of r that are greater than 1 are divisible by 5.

(2) There are exactly four different, positive integers that are factors of r.
[Reveal] Spoiler: OA

Last edited by Bunuel on 21 Mar 2013, 04:56, edited 1 time in total.
Renamed the topic and edited the question.

Kudos [?]: 1110 [0], given: 325

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41631

Kudos [?]: 124106 [1], given: 12071

Re: It is known that cuberoot (r) is a positive integer [#permalink]

Show Tags

New post 21 Mar 2013, 05:04
1
This post received
KUDOS
Expert's post
It is known that \(\sqrt[3]{r}\) is a positive integer. Is \(\sqrt[3]{r}\) a prime number?

Given that \(\sqrt[3]{r}=integer\) --> \(r=integer^3\) --> r is a perfect cube.

(1) All the factors of r that are greater than 1 are divisible by 5. If \(r=5^3\), then \(\sqrt[3]{r}=5=prime\) but if \(r=5^6\), then \(\sqrt[3]{r}=25\neq{prime}\). Not sufficient.

(2) There are exactly four different, positive integers that are factors of r. In order r to have 4 factors it must be of the form of \(r=prime^3\) and in this case \(\sqrt[3]{r}=\sqrt[3]{prime^3}=prime\) OR it must be of the form \(r=ab\), where a and b are primes (in this case the number of factors (1+1)(1+1)=4), but in this case r is NOT a perfect suqre, so this case is out. Sufficient.

Answer: B.

THEORY.
Finding the Number of Factors of an Integer

First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.

The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)

Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 124106 [1], given: 12071

Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 629

Kudos [?]: 1316 [0], given: 136

Premium Member
Re: It is known that cuberoot (r) is a positive integer [#permalink]

Show Tags

New post 21 Mar 2013, 05:09
guerrero25 wrote:
It is known that \(\sqrt[3]{r}\) is a positive integer. Is \(\sqrt[3]{r}\) a prime number?

(1) All the factors of r that are greater than 1 are divisible by 5.

(2) There are exactly four different, positive integers that are factors of r.


We have \(\sqrt[3]{r}\) is an integer.

From F.S 1, for r = \(5^3\), we have \(\sqrt[3]{5^3}\) = 5,a prime. So a YES for the question stem.Again, for r =\(5^6\),we have \(\sqrt[3]{5^6}\) = 25,not a prime. Insufficient.

From F.S 2, we have there are 4 factors for r. Thus, r can only be of the form

r = \(a*b\)or r = \(a^3\), where a,b are primes. For the former one, we wont have \(\sqrt[3]{r}\) as an integer. Thus, only the latter form is valid. Now, for r = \(a^3\), \(\sqrt[3]{r}\) = a, which is a prime. Sufficient.

B.

Ignore.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Kudos [?]: 1316 [0], given: 136

Expert Post
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7608

Kudos [?]: 16884 [0], given: 230

Location: Pune, India
Re: It is known that cuberoot (r) is a positive integer [#permalink]

Show Tags

New post 22 Mar 2013, 02:29
Expert's post
1
This post was
BOOKMARKED
guerrero25 wrote:
It is known that \(\sqrt[3]{r}\) is a positive integer. Is \(\sqrt[3]{r}\) a prime number?

(1) All the factors of r that are greater than 1 are divisible by 5.

(2) There are exactly four different, positive integers that are factors of r.



Note the takeaway from this question: All the factors (greater than 1) of a number, n, will not be divisible by the same prime number (other than 1) until and unless the number n is a power of that prime number.
This is so because if the number n has 2 prime factors, then there will be factors which have only one of those two primes. If every factor (other than 1) is divisible by the same prime, then the number has only one prime factor.

Ensure that you jot down such logical takeaways when you come across them during practice. Revisiting them again and again will help you build strong fundamentals. You keep joining the dots; the picture will become clear.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 16884 [0], given: 230

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 17563

Kudos [?]: 270 [0], given: 0

Premium Member
Re: It is known that cuberoot (r) is a positive integer [#permalink]

Show Tags

New post 08 Sep 2017, 22:37
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

Kudos [?]: 270 [0], given: 0

Re: It is known that cuberoot (r) is a positive integer   [#permalink] 08 Sep 2017, 22:37
    Similar topics Author Replies Last post
Similar
Topics:
4 EXPERTS_POSTS_IN_THIS_TOPIC If r and s are positive integers, is r/s an integer? 1) agdimple333 6 30 Jan 2016, 02:25
23 EXPERTS_POSTS_IN_THIS_TOPIC If r and s are positive integers, is r/s an integer? chicagocubsrule 19 09 Apr 2017, 19:07
6 EXPERTS_POSTS_IN_THIS_TOPIC Is integer R positive? Fairness 10 05 May 2015, 06:00
The positive integers r, s, and t are such that r is jamifahad 2 07 Sep 2011, 02:44
18 EXPERTS_POSTS_IN_THIS_TOPIC The positive integers r, s, and t are such that r is mehdiov 12 08 Aug 2017, 09:02
Display posts from previous: Sort by

It is known that cuberoot (r) is a positive integer

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.