Hello Vjesus12.
Let's take a look at your question. We want to find the value of $$\frac{2x}{3y}=?$$
First of all, we need to assume that x and y are integers.
First Statement
(1) x^2/y^2 = 36/25
Here we can get at least two different cases:
(i) x=6 and y=5, then $$\frac{2x}{3y}=\frac{2\left(6\right)}{3\left(5\right)}=\frac{4}{5}.$$
(ii) x=-6 and y=5, then $$\frac{2x}{3y}=\frac{2\left(-6\right)}{3\left(5\right)}=-\frac{4}{5}.$$
Since we get two different answers, then this statement
is not sufficient.
Second Statement
(2) x^5/y^5 > 1
This statement just tells us that x and y have the same sign. So, x and y can be any value. Therefore, this statement
is not sufficient.
First Statement + Second Statement
(1) x^2/y^2 = 36/25
(2) x^5/y^5 > 1
From both statements, we get that x and y have the same sign, therefore we can get just the two following cases:
(i) x=6 and y=5, then $$\frac{2x}{3y}=\frac{2\left(6\right)}{3\left(5\right)}=\frac{4}{5}.$$
(ii) x=-6 and y=-5, then $$\frac{2x}{3y}=\frac{2\left(-6\right)}{3\left(-5\right)}=\frac{4}{5}.$$
So, we get only one answer. Therefore, using both statements together
is sufficient.
I hope it helps.
