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# If x is positive, is x prime?

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Intern
Joined: 17 Jan 2016
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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:

27% (00:58) correct 73% (01:10) wrong based on 125 sessions

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If x is positive, is x prime?

(1) $$x^3$$ has exactly four distinct factors
(2) $$x^2-x-6=0$$
[Reveal] Spoiler: OA
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Joined: 02 Aug 2009
Posts: 5649
Re: If x is positive, is x prime? [#permalink]

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02 Apr 2016, 08:49
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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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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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Re: If x is positive, is x prime? [#permalink]

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

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04 Apr 2016, 10:21
Bunuel can you pls help us here?
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Re: If x is positive, is x prime? [#permalink]

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04 Apr 2016, 10:37
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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?
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If x is positive, is x prime? [#permalink]

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04 Apr 2016, 11:48
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?

Last edited by brockr1 on 05 Apr 2016, 01:51, edited 1 time in total.
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Re: If x is positive, is x prime? [#permalink]

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

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04 Apr 2016, 18:13
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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
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Re: If x is positive, is x prime? [#permalink]

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

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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..
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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

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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.
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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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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,
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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?   [#permalink] 02 Feb 2018, 07:49
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