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16 Sep 2014, 01:28
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If \(x\) and \(y\) are positive integers and \(\frac{x}{y}\) is an even integer, which of the following cannot be an odd integer?
A. \(y\)
B. \(x + y\)
C. \(y - 1\)
D. \(xy\)
E. \(y^2\)
A. \(y\)
B. \(x + y\)
C. \(y - 1\)
D. \(xy\)
E. \(y^2\)
16 Sep 2014, 01:28
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Official Solution:
If \(x\) and \(y\) are positive integers and \(\frac{x}{y}\) is an even integer, which of the following cannot be an odd integer?
A. \(y\)
B. \(x + y\)
C. \(y - 1\)
D. \(xy\)
E. \(y^2\)
Given: \(\frac{x}{y} = even\). This means \(x = y*even\). Since \(y\) is an integer, \(x\) must be even. Thus, \(xy\) (option D) is always even.
To discard options A, B, and E, consider \(x = 6\) and \(y = 3\).
To discard option C, consider \(x = 4\) and \(y = 2\).
Answer: D
If \(x\) and \(y\) are positive integers and \(\frac{x}{y}\) is an even integer, which of the following cannot be an odd integer?
A. \(y\)
B. \(x + y\)
C. \(y - 1\)
D. \(xy\)
E. \(y^2\)
Given: \(\frac{x}{y} = even\). This means \(x = y*even\). Since \(y\) is an integer, \(x\) must be even. Thus, \(xy\) (option D) is always even.
To discard options A, B, and E, consider \(x = 6\) and \(y = 3\).
To discard option C, consider \(x = 4\) and \(y = 2\).
Answer: D
21 Oct 2023, 13:25
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I've revised the question and solution, incorporating additional details for improved clarity. I trust this makes it more comprehensible.
