Value of Z

Finding out if 1/z > 1 actually refers to finding out if z is greater than 1 or not.
1. is not sufficient: for instance 1*0,5*2 = 1, giving you z = 2 > 1. But you could have 1*2*0,5, with z = 0.5 <1.
2. is again not sufficient: 1*0,25*4 = 1, with z either 2 or -2. Since you have two possible values for z from this example alone, then 2 by itself is obviously insufficient.

Taken together, the two statements shed some light on the problem. Since from 1 you get that xyz = 1, then xy*z^2 = xyz*z = 1*z = z. This means that z > 1, which is the equivalent of 1/z < 1.

Statement 1 alone is insufficent.
Statement 2 alone is insufficent.

Statement 1 tells us that z = 1/xy

We can substitute z with 1/xy from statement 1 to statement 2:
xy*(1/xy)^2>1. This would yield xy*(1/(xy)^2)>1. From this, we can deduce that 1/xy>1 or 1/z>1.

Hope this helps.

1/z>1 => z<1.

1. x*y*z=1 => this value depends on x and y also so z can be less or more than one. not suff.


2. same as 1st options, it is not suff.


taking togather.
from 2). xyz^2>1 => xyz*z>1
but xyz=1 from 1). replacing this value.

1.z>1 => z>1 -- Suff.

Anser - C.

is it allowed to divide inequalities??
if yes

dividing 1 by 2 gives 1/z > 1

any math wiz pl help...