谢谢，请指点思路。

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

Answer: E

X可以表述为5m+3 或7n+4, Y一样。即当5m+3=7n+4时可以求出X 或Y。即5m=7n+1时成立。若要被5整除，n只能是2,12,22,32.....或7,17,27,37.....因为这样7n+1的个位数是0或5。当n=2时，以上等式成立，可算出X，Y的最小值是18。次小的n值是7，可算出X，Y的次小值是53。这样X-Y=53-18=35即答案。

这个法子比较苯了，希望管用。