"j is divisible by 12 and 10" means that there is some integer n such that j = 2*2*3*5*n.

"j is divisible by 24" means that there is some integer m such that j =2*2*2*3*m.

Consider n=1.so j = 60. j **IS NOT** divisible by 24.

Consider n=2 so j =120. j **IS** divisible by 24 with m = 5

Consider n=3 so j = 180 j **IS NOT** divisible by 24.

Consider n=4 so j = 240 j **IS** divisible by 24, with m=10

. . .

Consider n=10 and j = 600 j **IS** divisible by 24 with m = 25

because 2*2*3*5*n = 2*2*2*3*m

5*n = 2*m

has integer values of (n,m) for (2,5), (4,10), (6,15), . . .

The answer is "**can't be determined.**" This is because **n must be even** (that is, **n has a prime factor of 2**).

This statement is always true:

If j is divisible by 24 and 20 then j is divisible by 24 (**how obvious is that?**).