In choice A Z can take any value greater than Zero.

If it is between (0,1) then its sq root will have greater value than z while if it is [1,∞) then sq root of z will be less than z.

In B we know that sq root of z is less than one and by question stem we know that sq root is greater than 0 so √z will be greater than z.

I understand hemanstood. But what will the answer be: C or B.
I guess it should be C, as we don't deal with sq. roots of negative numbers in GMAT, am i right??

Hi hijazim, I understood hemantsood explanation. Let’s see if I can help you..

(i) statement one doesn’t say much. Z could be a fraction or an integer >1, so the answer for “is sq.root Z greater than Z”? could be yes or no. explanation below..

(ii) - Sq.root Z is less than one.
We know that sq.root Z is greater than zero (statement). [f you have sq.root of 4, the answer is just 2 (-2 is eliminated by the statement)]

So, to find a sq.root <1, Z needs to be less than one and greater than zero ( 0<sq.root Z<1 ).

The answer for “is sq.root Z greater than Z”? YES, because sq.root of a fraction is bigger than the fraction (the opposite for integers >= one).

Example:
Sq.root 1/2 = 3/4, or sq.root 0.5=0.75. so, 1/2<sq.root1/2. (when you multiple positive fractions they get smaller..)
- try a integer >=1 to see the opposite relation..

Answer B (statement i doesn’t add, because for the sq.root of Z to be something, Z needs to be greater than zero, otherwise the sq.root is undefined for the gmat).

Hope this helps..

Thanks gbb. But i guess this question is not clear enough, as both C and B would be right in mathematics talking, but as GMAT does only deal with real numbers then statement A adds nothing to the solution.