integers

[ketkoag]

If X, Y, and Z are positive integers, is Y>X?
(1) Y^2=XZ
(2) Z-X>0

i got this ques correct but i did it by assuming the values, could any one tell me is there any better way to do solve this.

[Uri]

is the OA (C)?

(1) y^2=z.x
if y=4, z=16, then x=1. so, y>x
if y=4, z=1, then x=16. so, y<x
insufficient.

(2) no info about y. insufficient.

(1) & (2):
from (2) we know that z>x
let us assume, for a moment, that z=x, which is the maximum value possible.
then y=z=x (from st. 1)
but actually x<z. so x<y
sufficient.

[Musiq]

If X, Y, and Z are positive integers, is Y>X?
(1) Y^2=XZ
(2) Z-X>0

i got this ques correct but i did it by assuming the values, could any one tell me is there any better way to do solve this.

Is Y >X ?

Statement II:
No information about Y....so Insufficient...but restate the statement for further use ( if necessary)
Z - X > 0
Or, Z > X

Statement I:
(Y) (Y) = (X) ( Z)

For Y to be greater than X, we need to knwo more about Z.....but we dont.

Combining:
(Y) (Y) = (X) ( A number greater than X)
oR, (Y) ^2 = A number greater than (X) ^2

Since we are only asked to consider positive integers, this necessarily simplifies to Y > X.

Answer = C

NOTE:
I showed this explanation because you asked for a mathematical explanation....but Picking Number is the not a bad alternative method to use here.

[ketkoag]

OA is C

[kanha81]

If X, Y, and Z are positive integers, is Y>X?
(1) Y^2=XZ
(2) Z-X>0

i got this ques correct but i did it by assuming the values, could any one tell me is there any better way to do solve this.

(1) Y^2=XZ
No inform. abt relationship among x, y, z
Insuff

(2) Z-X>0
=> z > x
No inform. about y

(1) & (2)-
z = y^2 / x

((y^2) / x) > x
(y^2) > (x^2)
y > +/- x, but x>0
y > x

Suff
[spoiler][C][/spoiler]