CAT 2018 Quant Questions

Question:
Given that x2018y2017 = 1/2 and x2016y2019 = 8, the value of x2 + y3 is

35/4
37/4
31/4
33/4
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Correct Answer: 4

Given that $x^{2018}y^{2017}=\frac{1}{2}$ ... (1)

$x^{2016}y^{2019}=8$ ... (2)

Equation (2)/ Equation (1)

$\frac{y^2}{x^2} = \frac{8}{1/2}$

$\frac{y}{x} = 4$ or $-4$

Case 1: When $\frac{y}{x} = 4$

$x^{2018}(4x)^{2017}=\frac{1}{2}$

$x^{2018+2017}(2)^{4034}=\frac{1}{2}$

$x^{4035}=\frac{1}{(2)^{4035}}$

$x=\frac{1}{2}$

Since, $\frac{y}{x} = 4$, => y = 2

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

Case 2: When $\frac{y}{x} = -4$

$x^{2018}(-4x)^{2017}=\frac{1}{2}$

$x^{2018+2017}(2)^{4034}=\frac{-1}{2}$

$x^{4035}=\frac{1}{(-2)^{4035}}$

$x=\frac{-1}{2}$

Since, $\frac{y}{x} = -4$, => y = 2

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

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CAT 2018 Quant Questions
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