If \(x, y\) and \(z\) are positive integers, is \(x\%\) of

[Gmat_mission]

If \(x, y\) and \(z\) are positive integers, is \(x\%\) of \(y\) bigger than \(y\%\) of \(z?\)

(1) \(x= z\)
(2) \(z -y = y - x\)

[spoiler]OA=A[/spoiler]

Source: GMAT Club Tests

[deloitte247]

repeated by an error in posting...

[deloitte247]

$$x\%\ of\ y=\frac{x}{100}\cdot y$$
$$y\%\ of\ z=\frac{y}{100}\cdot z$$
Question=> Is x% of y bigger than y% of z?
$$\frac{x}{100}\cdot y>\frac{y}{100}\cdot z$$
Divide through by y/100
$$We\ have\ x>z$$
Statement 1: x = z
If x=z, then the question becomes; is z>z?
No x=z and x% of y is not bigger than y% of z. Thus, statement 1 is NOT SUFFICIENT.

Statement 2: z-y = y-x
z+x = y+y
z+x = 2y
The possible solution include z=4, y=3 and x=2.
If z=4, y=3, and x=2, then x<z but if z=2, y=3 and x=4, then x>z.
Since we cannot decide if x is greater or less than z, then, statement 2 is NOT SUFFICIENT.

Therefore, since statement 1 alone is SUFFICIENT, the correct answer is option A.