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16 Sep 2014, 00:28
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
65% (01:49) correct
35%
(01:55)
wrong
based on 754
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If \(x\) and \(y\) are integers and \(x=\frac{y}{5}+2\), is \(xy\) an even number?
(1) \(5x - 10\) is an even number
(2) \(\frac{y}{x}\) is an even number
(1) \(5x - 10\) is an even number
(2) \(\frac{y}{x}\) is an even number
16 Sep 2014, 00:28
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Official Solution:
If \(x\) and \(y\) are integers and \(x=\frac{y}{5}+2\), is \(xy\) an even number?
First, from the equation \(x=\frac{y}{5}+2\), we derive that \(y=5x-10\). Next, since \(x\) and \(y\) are integers, the product \(xy\) will be even if at least one of the factors is even. Therefore, the question essentially asks whether at least one of the unknowns, \(x\) or \(y\), is even.
(1) \(5x - 10\) is an even number.
Since \(y=5x-10\), then \(y=5x-10=\text{even}\). Sufficient.
(2) \(\frac{y}{x}\) is an even number.
Given: \(\frac{y}{x}=\text{even}\), so \(y=x*\text{even}=\text{even}\). Sufficient.
Answer: D
If \(x\) and \(y\) are integers and \(x=\frac{y}{5}+2\), is \(xy\) an even number?
First, from the equation \(x=\frac{y}{5}+2\), we derive that \(y=5x-10\). Next, since \(x\) and \(y\) are integers, the product \(xy\) will be even if at least one of the factors is even. Therefore, the question essentially asks whether at least one of the unknowns, \(x\) or \(y\), is even.
(1) \(5x - 10\) is an even number.
Since \(y=5x-10\), then \(y=5x-10=\text{even}\). Sufficient.
(2) \(\frac{y}{x}\) is an even number.
Given: \(\frac{y}{x}=\text{even}\), so \(y=x*\text{even}=\text{even}\). Sufficient.
Answer: D
General Discussion
16 Dec 2016, 04:12
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Bunuel
Hi Bunuel,
What happens if x is 0?
