Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 18 Jul 2019, 23:49

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

If x is positive, is x prime? (1) x^3 has exactly four distinct posit

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56271
If x is positive, is x prime? (1) x^3 has exactly four distinct posit  [#permalink]

Show Tags

New post 21 Dec 2018, 02:22
1
8
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

17% (01:46) correct 83% (01:32) wrong based on 101 sessions

HideShow timer Statistics


Manager
Manager
avatar
S
Joined: 24 Nov 2018
Posts: 109
Location: India
GPA: 3.27
WE: General Management (Retail Banking)
Premium Member
Re: If x is positive, is x prime? (1) x^3 has exactly four distinct posit  [#permalink]

Show Tags

New post 21 Dec 2018, 03:40
Bunuel wrote:
If x is positive, is x prime?

(1) x^3 has exactly four distinct positive integer factors.
(2) x^2 - x - 6 = 0


Statement 1) if x is composite, say 10, x^3 will have different distinct positive integer factors. 10^3=(5^3*2^3)=(3+1)*(3+1)=16. It will have exactly four distinct positive integer factors when x is prime and also, it is given x is positive. Hence, Sufficient.

Statement 2) x^2-x-6=0. Breaking it down, (x-3)*(x+2)=0, x=3,-2, but x is positive. So, x=3, hence, prime. Sufficient.

Each is sufficient. IMO, Option D.
_________________
Kudos encourage discussions. Share it to amplify collective education!
Manager
Manager
avatar
S
Joined: 08 Oct 2018
Posts: 64
Location: India
GPA: 4
WE: Brand Management (Health Care)
Re: If x is positive, is x prime? (1) x^3 has exactly four distinct posit  [#permalink]

Show Tags

New post 22 Dec 2018, 07:37
Bunuel wrote:
If x is positive, is x prime?

(1) x^3 has exactly four distinct positive integer factors.
(2) x^2 - x - 6 = 0


I think there may be a gap in my conceptual understanding.
Statement 1: From what I understand distinct positive integer factors means number of factors of x^3
Consider 6^3
6 has 4 distinct factors, namely 1,2,3, & 6. Cube of 6 will have 1, 2, 3, 8(2^3), 4(2^2), 27(3^3), 9(3^2), 36(6^2), and 6^3, that is 9 distinct factors.
Is this understanding correct?

Consider 2^3
2 has 2 distinct factors: 2 & 1.
2^3 will have 8(2^3), 4, 2, &1, that is 4 distinct factors.
2 is a prime number. Hence statement (1) is sufficient.

Unable to understand why OA is B.
_________________
We learn permanently when we teach,
We grow infinitely when we share.
GMAT Club Legend
GMAT Club Legend
User avatar
D
Joined: 18 Aug 2017
Posts: 4247
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
If x is positive, is x prime? (1) x^3 has exactly four distinct posit  [#permalink]

Show Tags

New post Updated on: 23 Dec 2018, 18:17
Bunuel wrote:
If x is positive, is x prime?

(1) x^3 has exactly four distinct positive integer factors.
(2) x^2 - x - 6 = 0



from 1
x^3 has 4 distinct factors

so x=2,3
say 2^3= 8 = 3+1 = 4 factors
or 27= 3^3 = 3+1 = 4 factors


in sufficeint

from 2
x^2 - x - 6 = 0

(x-3)(x+2)
x=3,-2

so 3 is +ve and prime sufficient IMO B
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.

Originally posted by Archit3110 on 22 Dec 2018, 08:04.
Last edited by Archit3110 on 23 Dec 2018, 18:17, edited 2 times in total.
Manager
Manager
avatar
B
Joined: 10 Aug 2009
Posts: 65
Reviews Badge
If x is positive, is x prime? (1) x^3 has exactly four distinct posit  [#permalink]

Show Tags

New post 22 Dec 2018, 09:13
Archit3110 wrote:
Bunuel wrote:
If x is positive, is x prime?

(1) x^3 has exactly four distinct positive integer factors.
(2) x^2 - x - 6 = 0



from 1
x^3 has 4 distinct factors

so x=2,3
say 2^3= 8 = 3+1 = 4 factors
or 27= 3^3 = 3+1 = 4 factors

in sufficeint

from 2
x^2 - x - 6 = 0

(x-3)(x+2)
x=3,-2

so 3 is +ve and prime sufficient IMO B


How come statement 1 is not sufficient, when 2 and 3 are both primes?
_________________
Retaking gmat for second time, any re-takers please feel free to connect.
GMAT Club Legend
GMAT Club Legend
User avatar
D
Joined: 18 Aug 2017
Posts: 4247
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
If x is positive, is x prime? (1) x^3 has exactly four distinct posit  [#permalink]

Show Tags

New post Updated on: 23 Dec 2018, 19:37
1
ravikumarmishra wrote:
Archit3110 wrote:
Bunuel wrote:
If x is positive, is x prime?

(1) x^3 has exactly four distinct positive integer factors.
(2) x^2 - x - 6 = 0



from 1
x^3 has 4 distinct factors

so x=2,3
say 2^3= 8 = 3+1 = 4 factors
or 27= 3^3 = 3+1 = 4 factors

in sufficeint

from 2
x^2 - x - 6 = 0

(x-3)(x+2)
x=3,-2

so 3 is +ve and prime sufficient IMO B


How come statement 1 is not sufficient, when 2 and 3 are both primes?


ravikumarmishra

from 1 x can be (10)^1/3 , so x^3=10^1/3 or say x=10
also which is 2^1 * 5^1 = 2*2 = 4 factors .. so in sufficient..
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.

Originally posted by Archit3110 on 22 Dec 2018, 09:20.
Last edited by Archit3110 on 23 Dec 2018, 19:37, edited 2 times in total.
Manager
Manager
avatar
B
Joined: 10 Aug 2009
Posts: 65
Reviews Badge
Re: If x is positive, is x prime? (1) x^3 has exactly four distinct posit  [#permalink]

Show Tags

New post 22 Dec 2018, 10:07
That makes sense. Thanks, I don't know how I missed this scenario, K+1.
_________________
Retaking gmat for second time, any re-takers please feel free to connect.
Intern
Intern
avatar
B
Joined: 25 Jan 2013
Posts: 29
Location: United States
Concentration: General Management, Entrepreneurship
Schools: Johnson '21
If x is positive, is x prime? (1) x^3 has exactly four distinct posit  [#permalink]

Show Tags

New post 23 Dec 2018, 10:45
1
Quote:
How come statement 1 is not sufficient, when 2 and 3 are both primes?


ravikumarmishra

from 1 x can be 10 also which is 2^1 * 5^1 = 2*2 = 4 factors .. so in sufficient..[/quote]
--

if x is 10, then x^3 does not have 4 distinct factors. Only prime x^3 has 4 distinct factors. So, how come A is not valid?
Manager
Manager
avatar
B
Joined: 18 Apr 2018
Posts: 93
If x is positive, is x prime? (1) x^3 has exactly four distinct posit  [#permalink]

Show Tags

New post 23 Dec 2018, 11:23
I feel OA is wrong x can't be 10. When x is 10, x^3 will be 1000 and has 16 distinct factors which doesn't satisfy statement 1. Hi Bunuel, please help clarify if my understanding is correct. Thanks.

Posted from my mobile device
Manager
Manager
avatar
B
Joined: 17 Jun 2018
Posts: 56
Location: India
Schools: IMD '20
GPA: 2.84
WE: Engineering (Consulting)
Re: If x is positive, is x prime? (1) x^3 has exactly four distinct posit  [#permalink]

Show Tags

New post 23 Dec 2018, 11:35
1
IMO If we assume X=(15)^(1/3),then X^3=15=5*3 which also has total of 4 factors. It is not mentioned anywhere that X is a +ve integer.

Posted from my mobile device
Manager
Manager
avatar
B
Joined: 18 Apr 2018
Posts: 93
Re: If x is positive, is x prime? (1) x^3 has exactly four distinct posit  [#permalink]

Show Tags

New post 24 Dec 2018, 02:48
Thanks arpitkansal, I quite understand now.

Posted from my mobile device
GMAT Club Bot
Re: If x is positive, is x prime? (1) x^3 has exactly four distinct posit   [#permalink] 24 Dec 2018, 02:48
Display posts from previous: Sort by

If x is positive, is x prime? (1) x^3 has exactly four distinct posit

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





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