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If x^(1/3) is a positive integer, does x^(1/3) have more than two dist
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08 Apr 2012, 19:36
Question Stats:
62% (01:41) correct 38% (01:44) wrong based on 73 sessions
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If \(\sqrt[3]{x}\) is a positive integer, does \(\sqrt[3]{x}\) have more than two distinct integer factors? (1) 64 < x < 216 (2) x is divisible by 5. 1) 64^(1/3)=4 , 125^(1/3)=5, and 216^(1/3)=6. Since x^(1/3) is an integer, x must equal 5. 5 is a prime number and only has two factors 1 and 5. So the answer is NO. Hence sufficient.
2) X=5k. Well 1000=5*200. x^(1/3)=1000^(1/3)=10 , which has 1,2,5,10 as its factors. So the answer the question is YES. But we can also pick x=125=5*25. x^(1/3)=125^(1/3)=5, which has only two factors: 1 and 5. Hence the answer is NO. Hence INSUFF.
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Re: If x^(1/3) is a positive integer, does x^(1/3) have more than two dist
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08 Apr 2012, 22:51
b. x can be 125 or 125^3 thus x ^ (1/3) = 5 or 125, factors 1,5 or 1,5,25,125 so on.
hence Insufficient.
A it is.



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Re: If x^(1/3) is a positive integer, does x^(1/3) have more than two dist
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09 Apr 2012, 00:58
If \(\sqrt[3]{x}\) is a positive integer, does \(\sqrt[3]{x}\) have more than two distinct integer factors?(1) 64 < x < 216 > take the cube root: \(4<\sqrt[3]{x}<6\) > since given that \(\sqrt[3]{x}=integer\) then: \(\sqrt[3]{x}=5\). 5 has only 2 distinct positive factors: 1 and 5. Sufficient. (2) x is divisible by 5 > if \(\sqrt[3]{x}=5\) the answer is NO but if \(\sqrt[3]{x}=10\) the answer is YES. Not sufficient. Answer: A.
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Re: If x^(1/3) is a positive integer, does x^(1/3) have more than two dist
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13 Sep 2012, 04:04
alphabeta1234 wrote: If x^(1/3) is a positive integer, does x^(1/3) have more than two distinct integer factors? (1) 64 < x < 216 (2) x is divisible by 5. Cannot Find an OA: My Solution 1) 64^(1/3)=4 , 125^(1/3)=5, and 216^(1/3)=6. Since x^(1/3) is an integer, x must equal 5. 5 is a prime number and only has two factors 1 and 5. So the answer is NO. Hence sufficient.
2) X=5k. Well 1000=5*200. x^(1/3)=1000^(1/3)=10 , which has 1,2,5,10 as its factors. So the answer the question is YES. But we can also pick x=125=5*25. x^(1/3)=125^(1/3)=5, which has only two factors: 1 and 5. Hence the answer is NO. Hence INSUFF. Another way to look at the question. Basically question says Is x^(1/3) a prime number, if x^(1/3) is a positive integer? (1) x=5, which is a prime. > Sufficient (2) x=5k, where is a positive integer > x= 5,10....>Insufficient Answer A
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Re: If x^(1/3) is a positive integer, does x^(1/3) have more than two dist
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12 Jun 2016, 08:10
A
1) x=125 .so x^1/3 =5 only 1&5 as factors.Suff
2)x^1/3 can be 25 or 5 which has more than 2 and only 2 factors.Not Suff



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Re: If x^(1/3) is a positive integer, does x^(1/3) have more than two dist
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13 Jun 2016, 09:26
alphabeta1234 wrote: If x^(1/3) is a positive integer, does x^(1/3) have more than two distinct integer factors?
(1) 64 < x < 216 (2) x is divisible by 5.
x^1/3 is prime or not? (1) 64 < x < 216 64^1/3 < x^1/3 < 216 ^1/3 4<< x^1/3 <6 Since x^1/3 is an integer it will be 5 (prime). sufficient (2) x is divisible by 5. Well it can be 5 or any multiple of 5. not sufficient. A is the answer
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Re: If x^(1/3) is a positive integer, does x^(1/3) have more than two dist
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05 Apr 2019, 00:27
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Re: If x^(1/3) is a positive integer, does x^(1/3) have more than two dist
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