Posted - 11/30/2013 : 23:36:26 GMAT -official guide, #68 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 Answer is B) 4. OK, maybe I get "something". "If x and y are integers and X not= 0, then x is a divisor/factor of Y., if Y is =XN". So prob: N= 5x + 1,N=5x+1 and N= 7y + 3. and 5x=7y+2. In the answer it explains that the units digit for 5x must be a 5 or 0. "Ok" and 7y+2 in order to agree must have a units digit of 5 or 0. and so 7y must be either 3 or 8. "OK", and Y cannot be just any number, it starts with 4, then skips to 9, then 14. I am stuck on the next step: "and so Y= 5Z +4, what does "5Z+4" explain? 5x4 +4 =24, not a product that has a 0 or 5. Then "N=7y +3 = 7(5Z+4) +3, this works out to be "35Z+31". So the remainder of the answer makes no sense to me: "Therefore if k is a positive integer, N+K is a multiple of 35 when K= 4, 39, 74...and the smallest of these intgers is "4" answer B."