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# If x is positive, is x prime?

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Re: If x is positive, is x prime? [#permalink]
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]
Bunuel can you pls help us here?
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Re: If x is positive, is x prime? [#permalink]
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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]
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, 12:48.
Last edited by brockr1 on 05 Apr 2016, 02:51, edited 1 time in total.
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Re: If x is positive, is x prime? [#permalink]
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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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]
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]
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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Re: If x is positive, is x prime? [#permalink]
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]
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]
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]
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]
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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Re: If x is positive, is x prime? [#permalink]
Hi everyone,

here is how I tackled this one

If x is positive, is x prime?

Note that x is not supposed to be an integer

(1) x3
x
3
has exactly four distinct factors

if we plug in a prime the statement is valid. For example: X=2--> X^3=8 which has 4 factors

But

What if X=√8 (the root square has a power of 3). The result is the same but this is not a prime

Hence A not suff.

(2) x2−x−6=0

X=-2;3
Since we are given X=positive X=3

Suff

B
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