模考软件里一道数学题~有人会吗？怎么解？谢谢~

随风倒 · 发表于 2010-1-13 13:42:29

The integer m and p are such that 2<m<p and m is not a factor of p . If r is the remainder when p is divided by m, is r>1?
(1)The greatest common factor of m and p is 2.
(2)The greatest common multiple of m and p is 30.
模考软件的答案是A.

冷咖啡 · 发表于 2010-1-13 13:50:37

(2)The greatest common multiple of m and p is 30
~~~~~~what's this?

1) m and p have common factor 2, so m and p are even. the remainder must be >= 2
correct
2) the least common multiple? if so, m and p can be 5, and 6
also can be 10 and 15
hence, the remainder can equal to 1 or 5, incorrect

随风倒 · 发表于 2010-1-13 14:30:20

第二个条件是Least common multiple，显然LS已经看出来了。

谢谢，你的方法是对的。

sunlight841206 · 发表于 2010-1-13 17:18:20

不好意思，我觉得楼上的方法有问题：
1）“m and p have common factor 2, so m and p are even. the remainder must be > 2
correct”这是错误的，反例：m=4,p=6,r=1
2）“the least common multiple? if so, m and p can be 5, and 6
also can be 10 and 15”这是错的，与条件1“The greatest common factor of m and p is 2”相冲突。

我的解题方法：
1）最小公倍数（The greatest common multiple of m and p is 30.）：30=2*3*5；
2）最大公约数（The greatest common factor of m and p is 2.）：m=2*X，n=2*Y；
再综合最小公倍数：m=2*3,n=2*5。所以m=6,n=10,r=4

冷咖啡 · 发表于 2010-1-13 18:35:03

不好意思，我觉得楼上的方法有问题：
1）“m and p have common factor 2, so m and p are even. the remainder must be > 2
correct”这是错误的，反例：m=4,p=6,r=1
2）“the least common multiple? if so, m and p can be 5, and 6
also can be 10 and 15”这是错的，与条件1“The greatest common factor of m and p is 2”相冲突。

我的解题方法：
1）最小公倍数（The greatest common multiple of m and p is 30.）：30=2*3*5；
2）最大公约数（The greatest common factor of m and p is 2.）：m=2*X，n=2*Y；
再综合最小公倍数：m=2*3,n=2*5。所以m=6,n=10,r=4

-- by 会员 sunlight841206 (2010/1/13 17:18:20)

I have no idea what ur point is.

模考软件里一道数学题~有人会吗？怎么解？谢谢~

写错了唉，粗心

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