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i. is not sufficient. you above KillerSquirrel have illustrated a case in which the questioned equation results in false. I'll illustrate one in which the questioned equation results in true: z = -3, x = -2, y = 1. | x - z | =
| z | - | x |.......So in this case, | -2 - (- 3) | = | -3 | - | - 2|, 1=1. So, of course, if we have one answer in which we get true and one in which we get false, statement i is insufficient. I get E as the answer then. Because you spotted that statement ii is equivalent to i. I didn't catch that part. I thought at first B was the answer.

i. is not sufficient. you above KillerSquirrel have illustrated a case in which the questioned equation results in false. I'll illustrate one in which the questioned equation results in true: z = -3, x = -2, y = 1. | x - z | = | z | - | x |.......So in this case, | -2 - (- 3) | = | -3 | - | - 2|, 1=1. So, of course, if we have one answer in which we get true and one in which we get false, statement i is insufficient. I get E as the answer then. Because you spotted that statement ii is equivalent to i. I didn't catch that part. I thought at first B was the answer.

Actually, it's always true ... For statment (1) & (2)... Have a look at my link

i. is not sufficient. you above KillerSquirrel have illustrated a case in which the questioned equation results in false. I'll illustrate one in which the questioned equation results in true: z = -3, x = -2, y = 1. | x - z | = | z | - | x |.......So in this case, | -2 - (- 3) | = | -3 | - | - 2|, 1=1. So, of course, if we have one answer in which we get true and one in which we get false, statement i is insufficient. I get E as the answer then. Because you spotted that statement ii is equivalent to i. I didn't catch that part. I thought at first B was the answer.

zy<xy<0...This means that z<x<0>0 and z>x>0 if y<0. In other words, both z and x have to be the same sign.

[1] z<x>0 Both z and x are negative - sufficient.

[2] kookoo4tofu wrote "y is greater than 0", but I believe the correct stmt is y<0. Using this stmt, both z and x are positive and therefore sufficient.

didn't you guys see that two cases have been advanced in which statement i produces a result of true and also a result of false? that disproves your claim.