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.
Value of Z
This topic has expert replies
Source: Beat The GMAT — Data Sufficiency |
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.
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.
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.
Shubham.
590 >> 630 >> 640 >> 610 >> 600 >> 640 >> 590 >> 640 >> 590 >> 590
590 >> 630 >> 640 >> 610 >> 600 >> 640 >> 590 >> 640 >> 590 >> 590
