TT-11-8

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Q8:

When positive integer x is divided by 5, the remainder is 3; and when x is divided by 7, the remainder is 4.  When positive integer y is divided by 5, the remainder is 3; and when y is divided by 7, the remainder is 4.  If x > y, which of the following must be a factor of x - y?

A.     12

B.     15

C.     20

D.     28

E.      35

我不知道你用什么方法，我是这样想的，如果5的倍数和7的倍数相差1（4-3)，那么7的这个倍数一定是9或者4结尾，因为5的倍数一定是0和5结尾。所以列举7的倍数得出49和84这两个数，它们之间的差为35。

根据条件推出：

X=5m+3

X=7n+4

y=5a+3

y=7b+4

then:

x-y=5(m-a)

and

x-y=7(n-b),

这证明x-y必须同时满足被5和7整除，而5和7互质，所以必被最小公倍数35整除