poweroc wrote:When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 35?

A - 3
B - 4
C -12
D - 32
E - 35

I have a lot of trouble with these types of questions and the OG answer is quite confusing. Thanks

k+n = 35, therefore, n = 35 - k

Any multiple of 35 would be divisible by 5 therefore k cannot be 3 because n needs to be a multiple of 5 - 1. E.g. if you take the smallest multiple of 35, i.e. 35 itself you can see that if n + k =35 and since we know n-1 is a multiple of 5, then k can't be 3 because that would make n-2 a multiple of 5. If you try with 4 you see that n would be equal to 31 and it fits both criteria, n-1 is a multiple of 5 (30) and n-3 is a multiple of 7 (28).