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vomhorizon
Joined: 03 Sep 2012
Last visit: 30 Mar 2018
Posts: 352
Given Kudos: 47
Location: United States
Concentration: Healthcare, Strategy
Schools: Duke '16 (A) McCombs '20 (A) Foster '20 (A)
GMAT 1: 730 Q48 V42
GPA: 3.88
WE:Medicine and Health (Healthcare/Pharmaceuticals)
Updated on: 05 Dec 2012, 06:30
Originally posted by vomhorizon on 05 Dec 2012, 06:24.
Last edited by Bunuel on 05 Dec 2012, 06:30, edited 1 time in total.
Last edited by Bunuel on 05 Dec 2012, 06:30, edited 1 time in total.
Renamed the topic and edited the question.
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A
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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
(1) x is divisible by exactly 3 positive integers
(2) All positive factors of x are odd
05 Dec 2012, 06:42
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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. 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.
Answer: A.
(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.
Answer: A.
vomhorizon
Joined: 03 Sep 2012
Last visit: 30 Mar 2018
Posts: 352
Own Kudos:
Given Kudos: 47
Location: United States
Concentration: Healthcare, Strategy
Schools: Duke '16 (A) McCombs '20 (A) Foster '20 (A)
GMAT 1: 730 Q48 V42
GPA: 3.88
WE:Medicine and Health (Healthcare/Pharmaceuticals)
05 Dec 2012, 06:57
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Thanks for the clarification..
