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# If x is positive, is x prime?

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Current Student
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If x is positive, is x prime?  [#permalink]

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02 Apr 2016, 08:34
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Difficulty:

95% (hard)

Question Stats:

25% (01:33) correct 75% (01:37) wrong based on 158 sessions

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If x is positive, is x prime?

(1) $$x^3$$ has exactly four distinct factors
(2) $$x^2-x-6=0$$
Math Expert
Joined: 02 Aug 2009
Posts: 7212
Re: If x is positive, is x prime?  [#permalink]

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02 Apr 2016, 08:49
3
3
krodin wrote:
If x is positive, is x prime?
(1) $$x^3$$ has exactly four distinct factors
(2) $$x^2-x-6=0$$

Hi,
1 is not suff because we do not know if x is an integer..
1) Say x^3 =6..
Factors of 6 are 1,2,3,6...
But x here is $$\sqrt[3]{6}$$..
Insuff

2)$$x^2-x-6=0$$
X=-2and 3...
X is positive so x=3
Suff

B
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If x is positive, is x prime?  [#permalink]

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04 Apr 2016, 05:01
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If x is positive, is x prime?
(1) x^3 has exactly four distinct factors
(2) x^2−x−6=0

In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make the answer D.
For 1), the number of factors is 3+1=4 and x must be prime, which is yes and sufficient.
For 1), from (x-3)(x+2)=0, x=3 is only possible, which is yes and sufficient.

 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 01 Jul 2010 Posts: 62 Location: India GMAT 1: 660 Q43 V38 GPA: 3.4 Re: If x is positive, is x prime? [#permalink] ### Show Tags 04 Apr 2016, 05:26 Hello Math Revolution, Infact i too marked D as the answer but it is wrong. The question states x is a positive number and not a positive integer. cube of $$\sqrt[3]{6}$$ can also have 4 factors but it is not a prime number -Arun Intern Joined: 07 Feb 2016 Posts: 6 Re: If x is positive, is x prime? [#permalink] ### Show Tags 04 Apr 2016, 10:21 Bunuel can you pls help us here? Math Expert Joined: 02 Sep 2009 Posts: 52389 Re: If x is positive, is x prime? [#permalink] ### Show Tags 04 Apr 2016, 10:37 1 1 Why2settleForLess wrote: If x is positive, is x prime? (1) $$x^3$$ has exactly four distinct factors (2) $$x^2-x-6=0$$ Bunuel can you pls help us here? Chetan's solution is spot on. Notice that we are not told that x is an integer. So, for (1) if x is an integer, then for x^3 to have 4 factors, x must be prime but if x is not an integer, for example, if $$x=\sqrt[3]{6}$$, then x is not a prime. Does this make sense? _________________ Current Student Joined: 17 Jan 2016 Posts: 17 Location: Russian Federation GMAT 1: 730 Q50 V38 GMAT 2: 750 Q49 V44 GPA: 3.3 If x is positive, is x prime? [#permalink] ### Show Tags Updated on: 05 Apr 2016, 01:51 All's clear, thank you all. Have I marked this question's difficulty correctly? Current stat is 14% of right answers, maybe it should be in 700+ category? Originally posted by brockr1 on 04 Apr 2016, 11:48. Last edited by brockr1 on 05 Apr 2016, 01:51, edited 1 time in total. Current Student Joined: 03 Jan 2014 Posts: 64 Concentration: Strategy, Operations GMAT 1: 720 Q46 V42 GPA: 3.86 WE: Information Technology (Consulting) Re: If x is positive, is x prime? [#permalink] ### Show Tags 04 Apr 2016, 15:51 Can you elaborate on why x^3 having 4 factors means it is prime? Is there a rule involving powers and factors giving us information on the primality of the number? Thanks! Math Expert Joined: 02 Aug 2009 Posts: 7212 Re: If x is positive, is x prime? [#permalink] ### Show Tags 04 Apr 2016, 18:13 1 sefienolte wrote: Can you elaborate on why x^3 having 4 factors means it is prime? Is there a rule involving powers and factors giving us information on the primality of the number? Thanks! Hi, if x is prime, then x^3 will have following factors 1,x,x^2 and x^3.. Also the formula for counting number of factors of any number is :- 1) first get the term in its prime factor. 2) number of factors = product of (power of prime +1) a)Here x is prime , so factor of x^3 = (3+1)=4 b)If x is not prime say it is 6.. 6^3 = 2^3*3^3.. number of factors=(3+1)(3+1)=4*4=16.. Hope it helps _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Current Student Joined: 29 Jun 2015 Posts: 11 Re: If x is positive, is x prime? [#permalink] ### Show Tags 06 Apr 2016, 01:18 krodin wrote: If x is positive, is x prime? (1) $$x^3$$ has exactly four distinct factors (2) $$x^2-x-6=0$$ Hi, Understood x^3 can be 6, which can have 4 factors; where x is not integer. But, my question is if it's asked, is x prime, doesn't that mean .. x has to be an integer, else how come x be a prime? Math Expert Joined: 02 Aug 2009 Posts: 7212 Re: If x is positive, is x prime? [#permalink] ### Show Tags 06 Apr 2016, 01:25 anchal25 wrote: krodin wrote: If x is positive, is x prime? (1) $$x^3$$ has exactly four distinct factors (2) $$x^2-x-6=0$$ Hi, Understood x^3 can be 6, which can have 4 factors; where x is not integer. But, my question is if it's asked, is x prime, doesn't that mean .. x has to be an integer, else how come x be a prime? Hi, If we are told x is PRIME , it would mean x is integer.. But since we are being asked IS X PRIME? and that x is positive, x can be anything positive.. In DS in GMAT, a VARIABLE can be anything except imaginary number, unless specified clearly.. _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6826 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x is positive, is x prime? [#permalink] ### Show Tags 06 Apr 2016, 05:15 raarun wrote: Hello Math Revolution, Infact i too marked D as the answer but it is wrong. The question states x is a positive number and not a positive integer. cube of $$\sqrt[3]{6}$$ can also have 4 factors but it is not a prime number -Arun Hi, The question probably is x is positive integer. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: If x is positive, is x prime?  [#permalink]

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06 Apr 2016, 05:27
MathRevolution wrote:
raarun wrote:
Hello Math Revolution,
Infact i too marked D as the answer but it is wrong.
The question states x is a positive number and not a positive integer.
cube of $$\sqrt[3]{6}$$ can also have 4 factors but it is not a prime number

-Arun

Hi,
The question probably is x is positive integer.

Why should x be a postive integer, when it is just given that it is positive..
it is perfectly fine as it is..
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If x is positive, is x prime?  [#permalink]

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07 Apr 2016, 07:24
krodin wrote:
If x is positive, is x prime?

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

please tell the source of this question..

Regards,
Current Student
Joined: 17 Jan 2016
Posts: 17
Location: Russian Federation
GMAT 1: 730 Q50 V38
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Re: If x is positive, is x prime?  [#permalink]

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07 Apr 2016, 11:22
debbiem wrote:
krodin wrote:
If x is positive, is x prime?

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

please tell the source of this question..

Regards,

Sorry I don't know the source. I took it from Russian gmat prep center's book which is compiled by their teachers from various sources like manhattan, og, etc.
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If x is positive, is x prime?  [#permalink]

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02 Feb 2018, 07:49
brockr1 wrote:
If x is positive, is x prime?

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

Statement I:

$$x = 2,3, 6^{1/3}$$
So, Insufficient.

Statement II:

$$x = 2,3$$.... So, Sufficient
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If x is positive, is x prime? &nbs [#permalink] 02 Feb 2018, 07:49
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