CAT 2018 [SLOT 1] Quant Question with Solution 03

$x^{2018} y^{2017}=\frac{1}{2}$…..(1)

and $x^{2016} y^{2019}=8$…..(2)

Dividing (1) by (2), $\frac{x^{2}}{y^{2}}=\frac{1}{16}$

$\frac{x}{y}=\frac{1}{4}$ i.e. $x=\pm \frac{1}{4} y$

$\left(\pm \frac{1}{4} y\right)^{2018} y^{2017}=\frac{1}{2}$

$y^{4035}=2^{4035}$

$y=2$

Therefore, $x=\pm \frac{1}{4}y=\pm \frac{1}{2}$

Hence, $x^{2}+y^{3}=\frac{1}{4}+8=\frac{33}{4}$