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16 Sep 2014, 01:26
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D
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Difficulty:
65%
(hard)
Question Stats:
52% (01:32) correct
48%
(01:26)
wrong
based on 266
sessions
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If \(x\) is a positive integer, is \(\sqrt{x}\) an integer?
(1) \(\sqrt{7*x}\) is an integer
(2) \(\sqrt{9*x}\) is not an integer
(1) \(\sqrt{7*x}\) is an integer
(2) \(\sqrt{9*x}\) is not an integer
16 Sep 2014, 01:26
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Official Solution:
If \(x\) is a positive integer, is \(\sqrt{x}\) an integer?
Crucial to know for the GMAT: if \(x\) is a positive integer, then \(\sqrt{x}\) is either a positive integer or an irrational number. (It cannot be a reduced fraction such as \(\frac{7}{3}\) or \(\frac{1}{2}\)).
Also, note that the question essentially asks whether \(x\) is a perfect square.
(1) \(\sqrt{7*x}\) is an integer.
This statement implies that \(x\) cannot be a perfect square, because if it is, for instance if \(x=n^2\) for some positive integer \(n\), then \(\sqrt{7x}=\sqrt{7n^2}=n\sqrt{7} \ne integer\). Sufficient.
(2) \(\sqrt{9*x}\) is not an integer.
Simplify: \(\sqrt{9*x}=3*\sqrt{x} \ne integer\), which implies that \(\sqrt{x} \ne integer\). Sufficient.
Answer: D
If \(x\) is a positive integer, is \(\sqrt{x}\) an integer?
Crucial to know for the GMAT: if \(x\) is a positive integer, then \(\sqrt{x}\) is either a positive integer or an irrational number. (It cannot be a reduced fraction such as \(\frac{7}{3}\) or \(\frac{1}{2}\)).
Also, note that the question essentially asks whether \(x\) is a perfect square.
(1) \(\sqrt{7*x}\) is an integer.
This statement implies that \(x\) cannot be a perfect square, because if it is, for instance if \(x=n^2\) for some positive integer \(n\), then \(\sqrt{7x}=\sqrt{7n^2}=n\sqrt{7} \ne integer\). Sufficient.
(2) \(\sqrt{9*x}\) is not an integer.
Simplify: \(\sqrt{9*x}=3*\sqrt{x} \ne integer\), which implies that \(\sqrt{x} \ne integer\). Sufficient.
Answer: D
General Discussion
07 Nov 2016, 10:32
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Statement 1: x is squareroot of an odd power of 7, so not an integer. Sufficient.
Statement 2: x is not a perfect square, hence its square root will not be an integer. Sufficient.
Statement 2: x is not a perfect square, hence its square root will not be an integer. Sufficient.
