求助prep一道~

huangsiyan

Integers m and p are such that 2<m<p,and m is not a factor of p.If r is the remainder by m, is r>1?
1The greatest common factor of m and p is 2.
2 The least common multiple of m and p is 30.

答案是A。不懂，没有思路，求解答！

arthurman

The question should read as "if r is the remainder when p is divided by m"

mereimoun

Basically m is not a factor of p, so p = m*n + r

r>0 for sure since m is not a factor of p.  But is r > 1?

1) The greatest common factor of m and p is 2.  If so, the difference between m and p is at least two.  In other words, they are not consecutive and they are both even numbers.  Then r has to be greater than 1! Because if r=1, then p is an odd number! so (1) is sufficient.

2) The least common multiple of m and p is 30. In this case, we do not know if m and p have common factors.  So this is not sufficient.  For example, m = 3, p = 10, then r =1.  However, m = 6, p = 10, then r = 4.

jingjane222

For condition 2, take note that:
30=2*3*5

huangsiyan

大家都是神人啊。。谢谢~