(i) xyz < 0 impilies that x,y, and z are non-zero and either one of the three values is negative with other two positive, or all three values are negative.

Case (a) x < 0
Then x < z < y so z is between x and y.

Case (b) z < 0.
Choose z = -1 , x = 1, y = 5. then z < x < y

So (i) is insufficient on it's own.

(ii) xy < 0 implies x, and y are non-zero, and one value is positive while the other value is negative.

Case (c) x > 0, y < 0
Choose y = -5, x = 1, z = 2. Then y < x < z

Case (d) x < 0, y > 0
Choose x = -1, y= 5, z = 1. Then x < z < y.

So (ii) is insufficient on it's own.

(i) and (ii) together implies that z > 0. So we have two cases.

Case (e) x > 0, y < 0
y < x < z

Case (f) x < 0, y > 0
x < y < z

So (i) and (ii) aren't sufficient together. Answer is E.

IMO E.

Ques is Z lie between X and Y.

lets go with easier statement first

Statement B says xy<0
that means either x is -ve and y is +ve or
x is +ve and y is -ve.
Not Suff. coz it dosen't say anything about Z.

Statement A tells us that xyz<0, Not suff. again.

Combining A and B is also again not suff.

Hope it helps...........