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16 Sep 2014, 00:42
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Is \(x*y*z\) an even integer?
(1) \(x*y\) is an even integer.
(2) \(y*z\) is an even integer.
(1) \(x*y\) is an even integer.
(2) \(y*z\) is an even integer.
16 Sep 2014, 00:42
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Official Solution:
Is \(x*y*z\) an even integer?
The key to solving this question is recognizing that we are not given that \(x\), \(y\), and \(z\) are integers.
(1) \(x*y\) is an even integer.
If the third variable, \(z\), is an integer, then \(x*y*z\) will certainly be even. However, if \(z\) is not an integer, then \(x*y*z\) will not necessarily be even. For instance, consider \(x*y=2\) and \(z=\frac{1}{3}\). Not sufficient.
(2) \(y*z\) is an even integer.
We can apply similar logic as above to conclude insufficiency.
(1)+(2) If \(x\), \(y\), and \(z\) are integers, for instance if \(x = y = z = 2\), then \(x*y*z\) will be even. However, \(x*y*z\) will not necessarily be an even integer, for instance consider \(x= y = z = \sqrt{2}\) or \(y=4\) and \(x=z=\frac{1}{2}\). Not sufficient.
Answer: E
Is \(x*y*z\) an even integer?
The key to solving this question is recognizing that we are not given that \(x\), \(y\), and \(z\) are integers.
(1) \(x*y\) is an even integer.
If the third variable, \(z\), is an integer, then \(x*y*z\) will certainly be even. However, if \(z\) is not an integer, then \(x*y*z\) will not necessarily be even. For instance, consider \(x*y=2\) and \(z=\frac{1}{3}\). Not sufficient.
(2) \(y*z\) is an even integer.
We can apply similar logic as above to conclude insufficiency.
(1)+(2) If \(x\), \(y\), and \(z\) are integers, for instance if \(x = y = z = 2\), then \(x*y*z\) will be even. However, \(x*y*z\) will not necessarily be an even integer, for instance consider \(x= y = z = \sqrt{2}\) or \(y=4\) and \(x=z=\frac{1}{2}\). Not sufficient.
Answer: E
