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# If root(x) is a positive integer is root(x) a prime number?

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Joined: 03 Sep 2012
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Kudos [?]: 105 [0], given: 31

If root(x) is a positive integer is root(x) a prime number? [#permalink]  05 Dec 2012, 05:24
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If $$\sqrt{x}$$ is a positive integer, is $$\sqrt{x}$$ a prime number?

(1) x is divisible by exactly 3 positive integers
(2) All positive factors of x are odd
[Reveal] Spoiler: OA

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Last edited by Bunuel on 05 Dec 2012, 05:30, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If root(x) is a positive integer is root(x) a prime number? [#permalink]  05 Dec 2012, 05:42
Expert's post
If $$\sqrt{x}$$ is a positive integer, is $$\sqrt{x}$$ a prime number?

(1) x is divisible by exactly 3 positive integers. The fact that $$x$$ has exactly 3 factors means that $$x=prime^2$$ (in this case the number of factors will be 2+1=3: 1, prime, and x. Check here: math-number-theory-88376.html). Therefore, $$\sqrt{x}=\sqrt{prime^2}=prime$$. Sufficient.

(2) All positive factors of x are odd. If $$x=1$$, then $$\sqrt{x}=1\neq{prime}$$ but if $$x=9$$ (9 has 3 odd factors: 1, 3, and 9), then $$\sqrt{x}=3={prime}$$. Not sufficient.

_________________
Current Student
Joined: 03 Sep 2012
Posts: 339
Location: United States
Concentration: Healthcare, Strategy
GMAT 1: 730 Q48 V42
GPA: 3.88
WE: Medicine and Health (Health Care)
Followers: 11

Kudos [?]: 105 [0], given: 31

Re: If root(x) is a positive integer is root(x) a prime number? [#permalink]  05 Dec 2012, 05:57
Thanks for the clarification..
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"When you want to succeed as bad as you want to breathe, then you’ll be successful.” - Eric Thomas

Re: If root(x) is a positive integer is root(x) a prime number?   [#permalink] 05 Dec 2012, 05:57
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