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?
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: bob9603 时间: 2012-3-21 23:21
芝麻来人作者: 泾渭不凡 时间: 2012-3-21 23:30 嗯~呵呵~打了一群汉字~还是觉得自己的方法不太清楚的说~还是帮bob同学找个正规解法啊~ 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.
谢谢饭饭姐啦O(∩_∩)O作者: 泾渭不凡 时间: 2012-3-21 23:56
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.
嗯~呵呵~打了一群汉字~还是觉得自己的方法不太清楚的说~还是帮bob同学找个正规解法啊~ 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.
