请教解法GWD
[font=Times New Roman][size=3]Q36:[/size][/font][font=Times New Roman][size=3]If [i]a[/i] and [i]b[/i] are positive integers such that [i]a[/i] – [i]b[/i] and a/b [/size][/font][size=3][font=Times New Roman]
are both even integers, which of the following must be an [u]odd[/u] integer?[/font][/size]
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[font=Times New Roman][size=3]A.[/size] [size=4]A a/2 B b/2 C (a+b)/2 D (a+2)/2 [/size][/font]
[font=Times New Roman][size=4] E E（b+2)/2 答案是D 想了几篇，还是不知道怎么理解 。。。。。 [/size][/font]
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[/size][/font] a-b is even, which means that the positive integers a and b are of the same kind(both odd or both even);
a/b is even, which means that a is even
considered that a and b are the same, so b is even too.
Considered all of the situations above, a=b(even)*c(even), which means 4 is a factor of a, because both b and c have a factor of 2
Lets say a=4m, So D=(a+2)/2=a/2+1=2m+1, which means it must be an odd integer 我的问题出在最后一个环节，谢谢您的点睛之笔。。。。呵呵
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