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16 Sep 2014, 01:24
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If \(m\) and \(n\) are positive integers, is \(m\) even?
(1) \(\frac{m}{n}\) is an odd integer.
(2) \(m + n\) is an even integer.
(1) \(\frac{m}{n}\) is an odd integer.
(2) \(m + n\) is an even integer.
16 Sep 2014, 01:24
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Official Solution:
If \(m\) and \(n\) are positive integers, is \(m\) even?
(1) \(\frac{m}{n}\) is an odd integer.
The above implies that \(m=n*\text{odd}\). Now, if \(n\) is odd, then \(m\) is also odd. However, if \(n\) is even, then \(m\) is also even. Not sufficient.
(2) \(m+n\) is an even integer.
The above implies that either both \(m\) and \(n\) are odd or both \(m\) and \(n\) are even. Not sufficient.
(1)+(2) Still the same two cases are possible: either both \(m\) and \(n\) are odd (for example \(m=3\) and \(n=1\)) or both \(m\) and \(n\) are even (for example \(m=2\) and \(n=2\)). Not sufficient.
Answer: E
If \(m\) and \(n\) are positive integers, is \(m\) even?
(1) \(\frac{m}{n}\) is an odd integer.
The above implies that \(m=n*\text{odd}\). Now, if \(n\) is odd, then \(m\) is also odd. However, if \(n\) is even, then \(m\) is also even. Not sufficient.
(2) \(m+n\) is an even integer.
The above implies that either both \(m\) and \(n\) are odd or both \(m\) and \(n\) are even. Not sufficient.
(1)+(2) Still the same two cases are possible: either both \(m\) and \(n\) are odd (for example \(m=3\) and \(n=1\)) or both \(m\) and \(n\) are even (for example \(m=2\) and \(n=2\)). Not sufficient.
Answer: E
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12 May 2018, 23:29
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Hi Bunuel,
I applied the generalized approach, Even No.* Even No. or Even No. * Odd No. = Even No.
The same outcomes are also applicable for division too, Because I had read about this rule somewhere, So I assumed, here as the outcome of Division is Odd, both No.s have to be Odd.
Is this rule for division correct ?
I applied the generalized approach, Even No.* Even No. or Even No. * Odd No. = Even No.
The same outcomes are also applicable for division too, Because I had read about this rule somewhere, So I assumed, here as the outcome of Division is Odd, both No.s have to be Odd.
Is this rule for division correct ?
