S1) j and k are consecutive integers, and consecutive integers share no factors except for 1. Sufficient.

S2) This leaves many possibilities. If jk=20, j=10 and k=2, the greatest common factor is 2. If jk=20, j=4 and k=5, the greatest common factor is 1. Insufficient.

Guess we could take the reverse route and see if we can eliminate by statements by proving insufficiency.

S1. j = k+1. try picking nos. (2,3) (3,4) (4,5) you'll also find that they're consecutive integers. The integers being odd and even the greatest common factor is always 1. So 1 always being the answer makes it sufficient.

S2. jk divisible by 5. Again substitute nos. for jk. jk could be 5,10,15,20,25. Were j and k both 5 then largest common factor would be 5. In other cases such as 10,15 the largest common factor of j n k (2,5) (3,5) would be one. so there is more than one answer for the largest factor. Makes the statement insufficient.

Got to be really mindful of not getting influenced by the first statement when solving for the second one.