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Difficulty:
15%
(low)
Question Stats:
77% (00:52) correct
23%
(01:08)
wrong
based on 158
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If x is a positive integer, is √√x an integer?
(1) x is the square of an integer.
(2) √x is the square of an integer.
(1) x is the square of an integer.
(2) √x is the square of an integer.
I agree with the OA. However, I have a doubt with (2):
\(\sqrt{x} = i^2\) , being \(i\) an integer.
Should we unsquare or use an additional square root on \(i\)? Is there a difference? I know that the square root only provide the positive root of the number.
Thanks!
\(\sqrt{x} = i^2\) , being \(i\) an integer.
Should we unsquare or use an additional square root on \(i\)? Is there a difference? I know that the square root only provide the positive root of the number.
Thanks!
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
03 Aug 2013, 08:46
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The question asks if \(x^{\frac{1}{4}}\) is a positive integer
(1) x is the square of an integer.
So x can be \(4\), and \(4^{\frac{1}{4}}\) is NOT a positive integer.
But x can be \(16\), and \(16^{\frac{1}{4}}\) is a positive integer.
Not sufficient
(2) \(\sqrt{x}\) is the square of an integer.
So \(\sqrt{x}=n^2\), \(x^{\frac{1}{4}}=n^{2*\frac{1}{2}}=n\) where n is an integer. Sufficient
Hope it's clear
(1) x is the square of an integer.
So x can be \(4\), and \(4^{\frac{1}{4}}\) is NOT a positive integer.
But x can be \(16\), and \(16^{\frac{1}{4}}\) is a positive integer.
Not sufficient
(2) \(\sqrt{x}\) is the square of an integer.
So \(\sqrt{x}=n^2\), \(x^{\frac{1}{4}}=n^{2*\frac{1}{2}}=n\) where n is an integer. Sufficient
Hope it's clear
30 Mar 2019, 11:23
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Using Statement 1, if x is the square of some integer n, then x = n^2. So we want to know if √√(n^2) = √n is an integer. We don't know, since we don't know if n itself is the square of an integer.
Using Statement 2, if √x is the square of some integer m, then √x = m^2. So we want to know if √√x = √(m^2) = m is an integer, and it is. So Statement 2 is sufficient.
Using Statement 2, if √x is the square of some integer m, then √x = m^2. So we want to know if √√x = √(m^2) = m is an integer, and it is. So Statement 2 is sufficient.
