number properties

x,y,z all positive,Is Z not between x and y ?

i.e x<z<y ?

(1) x <2z <y

here we can say x<2z & 2z < y

so z <y but z may be less than x INSUFF

(2) 4x <z <4y

4x < z & z <4y> x but z may be > y INSUFF

Combine 2z < y & 4x < z

so x < z < y SUFF

C

C

Used the same approach as samirpandit62.

I think a little different....
(1) If you divide x<2z<y by 2, you get x/2<z<y/2. If you sketch this latest inequality on a number line, you can see that you can have z between x and y, but you can also have z outside x and y. Therefore, not sufficient
(2) Using the number line again, you can see that 4x and 4y will always be to the right of x and y , because x and y are pozitive numbers. So, z will always be outside (on the right) of x and y. Thus the answer to the question will always be YES: Z is not between x and y.
Therefore B is the right choice.