Question : The third proportional of the following numbers $(x-y)^2, (x^2-y^2)^2$ is:

Option 1: $(x+y)^3(x-y)^2$

Option 2: $(x+y)^4(x-y)^2$

Option 3: $(x+y)^2(x-y)^2$

Option 4: $(x+y)^2(x-y)^3$

Question : If $x$ and $y$ are positive numbers such that $x - y = 5$ and $xy = 150$, the value of $(x + y)$ is:

Option 1: 45

Option 2: 25

Option 3: 35

Option 4: 15

Question : Let $x, y, z$ be fractions such that $x<y<z$. If $z$ is divided by $x$, the result is $\frac{5}{2}$, which exceeds $y$ by $\frac{7}{4}$. If $x+y+z=1 \frac{11}{12}$, then the ratio of $(z-x):(y-x)$ is:

Option 1: 6 : 5

Option 2: 9 : 5

Option 3: 5 : 6

Option 4: 5 : 9

Question : The ratio of the monthly incomes of X and Y is 5 : 4 and that of their monthly expenditures is 9 : 7. If the income of Y is equal to the expenditure of X, then what is the ratio of the savings of X and Y?

Option 1: 9 : 8

Option 2: 6 : 7

Option 3: 8 : 9

Option 4: 7 : 6

Question : If $x^{3}-y^{3}=81$ and $x-y=3$, what is the value of $x^{2}+y^{2}$?

Option 1: 18

Option 2: 21

Option 3: 27

Option 4: 36