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08 Apr 2012, 19:36
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
63% (01:52) correct
37%
(01:54)
wrong
based on 297
sessions
History
Date
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Not Attempted Yet
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 < 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.
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.
08 Apr 2012, 22:51
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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.
thus x ^ (1/3) = 5 or 125, factors 1,5 or 1,5,25,125 so on.
hence Insufficient.
A it is.
09 Apr 2012, 00:58
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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 --> 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.
(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.
