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标题: 输血寂静第12题，没看懂答案意思,小菜抱拳啦~~ [打印本页]

作者: rmbaos 时间: 2012-4-11 06:50 标题: 输血寂静第12题，没看懂答案意思,小菜抱拳啦~~

12. V1. 一个数除以5余3等，表达出来即x1=5a+3, x1=7b+4, x2=5c+3, x2=7d+4，然后是x1>x2，问x1,x2的最大公约数 (kdavid1945)

V2. 狗主回忆的版本信息貌似有误，下面是GWD原题，请大家看一下哈！
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
答案：x=18,53,88,123,...,35n+18，答案选E

小菜没有懂：35n+18哪里来的？还有前面的数是怎么出来的~~

作者: coloryao 时间: 2012-4-11 19:39

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

When the positive integer x is divided by 5 and 7, the remainder is 3 and 4, respectively: x=5q+3 (x could be 3, 8, 13, 18, 23, ...) and X=7p+4 (x could be 4, 11, 18, 25, ...).

There is a way to derive general formula based on above two statements:

Divisor will be the least common multiple of above two divisors 5 and 7, hence 35

Remainder will be the first common integer in above two patterns, hence 18--> so, to satisfy both this conditions x must be of a type x=35m+18 (18, 53, 88, ...);

The same for y (as the same info is given about y): y=35n+18 ; x-y=(35m+18)-(35n+18)=35(m-n) --> thus x-y must be a multiple of 35.

Answer: E.

作者: Sunfisher006 时间: 2012-4-12 06:51

这题我也问过，木有人鸟我啊。

作者: coloryao 时间: 2012-4-12 20:19

The difference must be the multiple of 35, which is LCM of 5 and 7.
1) In order for x and y to leave the same remainder when divided by 5, the gap between two numbers should be a multiple of 5.
2)In order for x and y to leave the same remainder when divided by 7, the gap between two numbers should be a multiple of 7.
But x and y leave the same remainders when divided by both 5 and 7...so the gap between x and y should be a multiple of 5 AND a multiple of 7 or simply it should be a multiple of 35, which is LCM (5,7).

The only number that is a multiple of 35 is E, hence E is an answer.

那个不太清晰就看这个~

作者: rmbaos 时间: 2012-4-13 06:54

i got it , thanks !@

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