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Current Student Joined: 17 Jan 2016
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Location: Russian Federation
GMAT 1: 730 Q50 V38 GMAT 2: 750 Q49 V44 GPA: 3.3
If x is positive, is x prime?  [#permalink]

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9 00:00

Difficulty:   95% (hard)

Question Stats: 29% (01:43) correct 71% (01:38) wrong based on 147 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 V
Joined: 02 Aug 2009
Posts: 8138
Re: If x is positive, is x prime?  [#permalink]

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3
5
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 $$\sqrt{6}$$..
Insuff

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

B
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Math Expert V
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Re: If x is positive, is x prime?  [#permalink]

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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 $$x=\sqrt{6}$$, then x is not a prime.

Does this make sense?
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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]

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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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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 $$\sqrt{6}$$ 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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Bunuel can you pls help us here?
Current Student Joined: 17 Jan 2016
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Location: Russian Federation
GMAT 1: 730 Q50 V38 GMAT 2: 750 Q49 V44 GPA: 3.3
If x is positive, is x prime?  [#permalink]

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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]

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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!
Current Student Joined: 29 Jun 2015
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Re: If x is positive, is x prime?  [#permalink]

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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,
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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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]

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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 $$\sqrt{6}$$ 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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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 $$\sqrt{6}$$ 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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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
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Re: If x is positive, is x prime?  [#permalink]

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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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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]

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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 Re: If x is positive, is x prime?   [#permalink] 11 Sep 2019, 12:35
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