When we compare \(A\) and \(B\), we can try to figure out \(A - B\) is positive or negative, since \(A > B\) is equivalent to \(A - B > 0\) and \(A < B\) is equivalent to \(A - B < 0\).

\(A - B = x(z-y) - y(z-x) = xz - xy - yz + xy = xz - yz = z(x-y) < 0\) since we have \(z > 0\) and \(x < y\).
Thus we have \(A < B\).

Therefore, \(B\) is the right answer.

Hi Guys,
Given that 0 < z and x<y..
But we have no relation between z and x or z and y right ?
for example let us consider z = 1,x=2,y=3.
It satisfies the two mentioned conditions.
x(z-y) = 2(1-3) = -2
y(z-x) = 3(1-2) = -3.
In this case A turns out to be greater..Can someone help me with this ? TIA

The fastest approach is the above explanation adopted by Brent

https://gre.myprepclub.com/forum/x-z-y-2397.html#p4422

However, you have to consider, if you want to pick up numbers and test them, both integers and fractions.

and also negative numbers in the case of y and x.

Moreover, they can be also the same numbers. Nothing in the stem mentions that they must be different

You only know that z is positive. y and x could be also negative

If test different scenarios, you will see that B is always > than A regardless of the fact that z has no relation with x and y

Lett me know if you need further assistance sir

x(z-y) = -4