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16 Sep 2014, 00:22
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If \(m\) and \(n\) are consecutive integers, is \(m\) greater than \(n\)?
(1) \(m-1\) and \(n+1\) are consecutive integers
(2) \(\frac{m}{n}\) is an even integer
(1) \(m-1\) and \(n+1\) are consecutive integers
(2) \(\frac{m}{n}\) is an even integer
16 Sep 2014, 00:22
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Official Solution:
If \(m\) and \(n\) are consecutive integers, is \(m\) greater than \(n\)?
(1) \(m-1\) and \(n+1\) are consecutive integers.
If \(m\) were less than \(n\), then \(m-1\) (an integer less than \(m\)) and \(n+1\) (an integer greater than \(n\)) wouldn't be consecutive. Hence, \(m\) must be greater than \(n\). Sufficient.
Or look at this in another way: the stem says that the distance between \(m\) and \(n\) is 1. Now, if \(m < n\), then the distance between \(m-1\) and \(n+1\) would be 3, and they couldn't be consecutive as (1) states. Thus, it must be true that \(m > n\).
(2) \(\frac{m}{n}\) is an even integer.
Could \(m\) be greater than \(n\)? Certainly. For instance, if \(m = 2\) and \(n = 1\), or if \(m = 0\) and \(n = -1\). However, \(m\) can also be less than \(n\), such as when \(m = -2\) and \(n = -1\), or if \(m = 0\) and \(n = 1\). Not sufficient.
Answer: A
If \(m\) and \(n\) are consecutive integers, is \(m\) greater than \(n\)?
(1) \(m-1\) and \(n+1\) are consecutive integers.
If \(m\) were less than \(n\), then \(m-1\) (an integer less than \(m\)) and \(n+1\) (an integer greater than \(n\)) wouldn't be consecutive. Hence, \(m\) must be greater than \(n\). Sufficient.
Or look at this in another way: the stem says that the distance between \(m\) and \(n\) is 1. Now, if \(m < n\), then the distance between \(m-1\) and \(n+1\) would be 3, and they couldn't be consecutive as (1) states. Thus, it must be true that \(m > n\).
(2) \(\frac{m}{n}\) is an even integer.
Could \(m\) be greater than \(n\)? Certainly. For instance, if \(m = 2\) and \(n = 1\), or if \(m = 0\) and \(n = -1\). However, \(m\) can also be less than \(n\), such as when \(m = -2\) and \(n = -1\), or if \(m = 0\) and \(n = 1\). Not sufficient.
Answer: A
General Discussion
16 Oct 2023, 09:41
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
