number properties

[sud21]

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 p and m is 2
2). The least common multiple of m and p is 30

[Anurag@Gurome]

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 p and m is 2
2). The least common multiple of m and p is 30

(1) The greatest common factor of p and m is 2 implies p and m are both even, which means the remainder will also be even (because when even is divided by even then we get an even integer). This definitely means that the remainder is always greater than 1; SUFFICIENT.

(2) The least common multiple of m and p is 30.
If m = 3 and p = 10, then the LCM = 30
If m = 5 and p = 6, then the LCM = 30
No definite answer; NOT sufficient.

The correct answer is A.