Division concept
The integers 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?
I. The greatest common factor of m and p is 2
II. the least common multiple of m and p is 30
Here, for statement 1, if m=6 and p=10, p/m=5/3 and remainder = 2
However, when m = 4 and p = 6, p/m = 3/2 and remainder = 1
How is A sufficient then?
In this question the fundamental fact is that when talking about remainders we do not convert fraction into their lowest terms.
For statement 1: m =4, p=6, r=2; m=6, p=10,r=4. Yes it is sufficient as there is no such case case. Since, their GCD is 2 both the numbers are even. As two even numbers will separated by at least 2 the remainder will be greater than 1. Hence, option A or D.
For statement 2: m=5, p =6, r =1. Insufficient, hence B eliminated. Together does not make sense as I is alone sufficient.
Therefore, option A.
