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# problem

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Intern
Joined: 18 Dec 2006
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26 Jun 2008, 08:19
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

if x positive, is x prime?
1) x3 has exactly four distinct factors.
2) x2-x-6=0

answer is B, is it ok?

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Current Student
Joined: 12 Jun 2008
Posts: 287

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Schools: INSEAD Class of July '10

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26 Jun 2008, 08:39

(2) is sufficient since it implies that x=3 and 3 is prime

(1) is sufficient too :

if x is not prime it has at least 2 factors that we can call a and b with a and b different from 1

Then a, b, a^2, a^3, b^2, b^3 are all different factors of x^3 (and there are more) : this is more than 4 factors.

Conclusion : not prime => more than 4 factors and thus 4 factors => prime

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Director
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26 Jun 2008, 08:40
is it x3 and x2 OR x^3 and x^2?

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Intern
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26 Jun 2008, 08:43
gmatnub, sorry
sure, you are right

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Intern
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26 Jun 2008, 08:45
thanks a lot, now is correct

if x positive, is x prime?
1) x^3 has exactly four distinct factors.
2) x^2-x-6=0

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Intern
Joined: 18 Dec 2006
Posts: 39

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26 Jun 2008, 08:49
2) it is clear

1) I think it is also enough, what is wrong here

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Manager
Joined: 20 Mar 2008
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26 Jun 2008, 08:51
It is D.

1) x^3 has only 4 factors --> only possible if x is prime.

2^3 is 8. It has factors 8,4,2,1 Only 4 factors
3^3 is 21. It has factors 27,9,3,1 Only 4 factors

works when x is prime

4^3 is 64. It has factors 64,32,16,8,4,2,1 Greater Than 4 factors
Edit : This explanation is WRONG! Check posts below.

2) x2-x-6=0
(x+2) (x-3)=0
x=3 or x=-2
QS tells us it is +ve x=3 => x is prime.

Last edited by vishy007 on 26 Jun 2008, 09:17, edited 1 time in total.

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SVP
Joined: 30 Apr 2008
Posts: 1863

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Location: Oklahoma City
Schools: Hard Knocks

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26 Jun 2008, 08:51
This question is from Kaplan GMAT 2005 with CD-ROM and the question as originally posted is not correct.

The correct question:

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

------------------------------------
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$. GMAT Club Premium Membership - big benefits and savings Kudos [?]: 623 [0], given: 32 SVP Joined: 30 Apr 2008 Posts: 1863 Kudos [?]: 623 [2], given: 32 Location: Oklahoma City Schools: Hard Knocks Re: problem [#permalink] ### Show Tags 26 Jun 2008, 08:52 2 This post received KUDOS OA is B. OE: We have a yes-no question, so we'll need to know if $$x$$ is always prime or never prime. When working with primes, keep in mind that 2 is the smallest prime number on the only even prime. Other than that, all we know from the stem is that $$x > 0$$, so let's evaluate the statements. (1) Insufficient. Can we find any prime values for x such that $$x^3$$ has 4 distinct factors? If $$x=2$$, which is prime, then $$x^3 = 2^3 = 8$$, which has 4 distict factors (1, ,2, 4, and 8). So it's possible that $$x$$ is prime. But does it have to be prime? Lets consider other positive numbers with 4 distinct factors. The smalelst such number is 6 (its factors are 1, 2, 3, and 6), so suppose $$x^3 = 6$$. In this case, $$x = \sqrt{6}$$, which is not even an integer, much less a prime number. So we've found both prime and non-prime values for $$x$$ that make (1) true. Therefore, (1) is insufficent to determine whether or not $$x$$ is prime. Eliminate (A) and (D). (2) Sufficient. In this case, we can solve the equation to find possible values for $$x$$. If we subtract 6 from both sides, we get $$x^2 - x - 6 = 0$$. Factor the left side using reverse FOIL to get (x-3)(x+2) = 0. So, the equation has one negative root and one positive root, meaning that there are two possible values for x, one negative and one positive. The stem tells us that $$x$$ must be positive, so there is actually only one possible value of $$x$$. Since we could find exactly one value for $$x$$, we can answer the question definitely, if we know what $$x$$ is, we know whether or not it is prime. So Statement (2) is sufficient. Answer B. _________________ ------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

GMAT Club Premium Membership - big benefits and savings

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Manager
Joined: 20 Mar 2008
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26 Jun 2008, 09:08
Oops!

I know this trap, yet I keep forgetting time and again.

jallenmorris, thanks for posting OE.

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Intern
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26 Jun 2008, 09:14
jallenmorris cool!!!
respect,
I didn't even try to do it from that side
thanks a lot, my friend
thanks to everybody

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Re: problem   [#permalink] 26 Jun 2008, 09:14
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# problem

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