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。
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。
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?
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！
条件1:x=12m+5 x=8m+4m+5 当m=1(奇数),余数为1,当m=2(偶数)时,m=5
条件2:x=18n+7 x=16n+2n+7 当m=1(奇数)时,余数为1,当m=2(偶数时，m=3
所以条件１和条件２可以推出，余数为１
| a | b=(2*a-1)/3 | c=12*a+5 | d=18*b+11 | MOD(C6,8) | |
| 2 | 1 | 29 | 29 | 5 | |
| 5 | 3 | 65 | 65 | 1 | |
| 8 | 5 | 101 | 101 | 5 | |
| 11 | 7 | 137 | 137 | 1 | |
| 14 | 9 | 173 | 173 | 5 | |
| 17 | 11 | 209 | 209 | 1 | |
| 20 | 13 | 245 | 245 | 5 | |
| 23 | 15 | 281 | 281 | 1 | |
| 26 | 17 | 317 | 317 | 5 | |
| 29 | 19 | 353 | 353 | 1 | |
| 32 | 21 | 389 | 389 | 5 | |
| 35 | 23 | 425 | 425 | 1 | |
| 38 | 25 | 461 | 461 | 5 |
answer should be E, coz the reminder could be either 1 or 5.
I just used EXCEL to prove my hypothsis, since I gotta the equation 2*a=3*b+1, thus each ai should be 3 greater than a (i-1). thus for each integer Ni, which equal to 12*ai+5, should be 36 greater than N(i-1). coz, 36 is not devidable by 8. the reminder could be compound.
and I used EXCEL to prove my solution. Yes, there are two probabilities.
THIS QUESTION IS SUCK
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?
条件1和2是矛盾的,不可能有一个x同时满足
如果条件2是, ......remainder is 11, 那么同时满足1和2的数字,其被8除的余数不唯一,所以选E
条件1和2是矛盾的,不可能有一个x同时满足
如果条件2是, ......remainder is 11, 那么同时满足1和2的数字,其被8除的余数不唯一,所以选E
显然你的观点不正确，你看看前面有个cicilla mm的回答非常精彩！
.
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。
X通项是：X=36m+29是怎么推出来了?哪位高人说说. 谢谢!!
请问cicilla:
1.you said: 但是n=(9m+1)/6 可以看出n,m没有整数解。所以无解??
2. you said:
除以8：余数有几个不同的值，所以选E.
怎么理解呢?
请问NN:
1. 但是n=(9m+1)/6 可以看出n,m没有整数解。所以无解??
if 有整数解, 就有解??
if so, why?
up, up!
NN help ....how to sovle such kind of question? Xianxieguole!!!
条件1:x=12m+5 x=8m+4m+5 当m=1(奇数),余数为1,当m=2(偶数)时,m=5
条件2:x=18n+7 x=16n+2n+7 当n=1时,余数为1,当n=2时，余3，n＝3，余5
（直接改了，xulijun请别介意）
所以条件１和条件２可以推出，余数为１。5
这个方法是万能的，我就是用这个方法算的，可惜xulijun没解完，
条件2继续下去，当n＝3时，余数为5，
条件1与条件2的交集是1，5，不唯一，故而选E
这个方法可以解所有的这类题，36m＋n的说法有许多不足，因为36的因子有2和3，而8与3是没有交集的，这种方法更适用于单一因子，比如，被8m＋n，被2。4除，都余n。
讨论请继续！
To windlake:
you haven't finished it, either.
条件1:x=12m+5 x=8m+4m+5 当m=1(奇数),余数为1,当m=2(偶数)时,m=5
条件2:x=18n+7 x=16n+2n+7 当n=1时,余数为1,当n=2时，余3，n＝3，余5
when n=4, 余7
所以条件１和条件２可以推出，余数为 1, 3.
Furthermore, in TS, this item should be:
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
therefore, by using your method:
条件1:x=12m+5 x=8m+4m+5 当m=1(奇数),余数为1,当m=2(偶数)时,m=5
条件2:y=18n+11 y=16n+2n+11 当n=1时,余数为5,当n=2时，余7，n＝3，余1, when n=4, 余3,when n=5, 余5, when n=6, 余7,when n=7, 余1, when n=8, 余3 so on and so forth
therefore,
条件1与条件2的交集是1,5，not唯一，故而选e. Great idea, though.
open to discuss....
if 条件1与条件2的交集是5，say, 唯一，will you choose C?
OR,
we need to confirm whether X is the same number?
otherwise, still can not satisfy both of them, right?
明白了,谢谢~
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