[求助]天山-3-32

Q32.

What is the remainder when the positive integer x is divided by 8?

(1) when x is divided by 12, the remainder is 5,

(2) when x is divided by 18, the remainder is 7.

How do solve this question?

这题对吗？

题意可知，设:

1.)   X=12n+5

2.)   X=18m+7

则12n+5=18m+7, 那么可得：  3(2n-3m)=1,  n,m 均为自然数，前式无解。。。。。。。

如果条件2改成：

(2) when x is divided by 18, the remainder is 17.

则：the remainder when X is divided by 8 is 7.

如果条件1改成：

(1) when x is divided by 12, the remainder is 15.

此题仍然无解。

Thank you very much!

The answer is E: Both together are not enough.

我的题目和你不一样，如下：

Q32:
What is the remainder when the positive integer x is divided by 8?
(1) When x is divided by 12, the remainder is 5.
(2) When x is divided by 18, the remainder is 11.

因此， 我选C。

x=12a+5=18b+11

当a=2, b=1, x=29.

请讨论。
  

a=5

b=3

x=65同样成立

谢谢！

糊涂。

可以尝试去写出X的通项：X=36m+Y  这里的Y是X能够取得最小的数，由12n+5=18m+7中，n,m最小的值决定。但是n=(9m+1)/6  可以看出n,m没有整数解。所以无解。选择E

同理：

What is the remainder when the positive integer x is divided by 8?

(1) when x is divided by 12, the remainder is 5,

(2) when x is divided by 18, the remainder is 11.

X通项是：X=36m+29

除以8：余数有几个不同的值，所以选E

bobwangwb: 题目问的是余数的数值是否可以求出来，不是说能不能整除。

谢谢cicilla，帮我解了不少题。

祝你考试顺利！