CITI29 wrote: 1)k =j+1

let's say k is a multiple of 2.
then the other multiples of 2 are 2, 4, 6, ... more than k, as well as 2, 4, 6, ... less than k.
so j, which is only 1 more than k, isn't one of those.

same goes if k is a multiple of 3, or 4, or ... any positive integer (except 1).

this reasoning proves that k and j don't share any common factors (other than the trivial 1), so their gcf is 1.

the above poster has stated, correctly, that one of k & j must be even and the other odd. however, that condition alone doesn't mean that the gcf must be 1: for instance, 9 is odd and 12 is even, but their gcf is most certainly not 1.

--

here's another clever way of thinking of the gcf: if the 2 numbers were the numerator and denominator of a fraction, what's the biggest # you could pull out of both to reduce the fraction?

if you make fractions out of these number pairs, in which one number is exactly 1 greater than the other - 7/8, 10/11, 18/19, etc. - it should be pretty clear to you that none of the resulting fractions are going to reduce.
that means the gcf is 1.

sufficient.

CITI29 wrote:2)jk is divisible by 5.

all this means is that at least one of j and k is divisible by 5. could be one or both of them, and, moreover, you know nothing whatsoever about divisibility by any other factors. so the gcf could actually be absolutely any number you want.

or, if you like easily accessible concrete #s:
j = 3, k = 5 --> jk = 15 is divisible by 5 --> gcf = 1
j = 10, k = 5 --> jk = 50 is divisible by 5 --> gcf = 5
insufficient

answer = b