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prep一道题,好像答案不对?

The integers m and p 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 greated common factor of m and p is 2

2)the least common multiple of m and p is 30

The answer of this question is A, but I choose D, because 2) is sufficient:

Under the condition of 2) the possible solution is m=3,p=10 or m=5,p=6 so r=1

Who can explain the ets answer to me?

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if m=10, p=15,then r=5>1

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thanks !!!!!

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