CAT 2018 Question Paper Shift 1 Solved Paper

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Question : 89 of 100

Marks: +1, -0

Given that

x^{2018}y^{2017}

= 1/2 and

x^{2016}y^{2019}

= 8, the value of

x^2 + y^3

is
Options

$33/4$
$37/4$
$31/4$
$35/4$

Solution:

x^{2018} y^{2017}=\;{1}/{2} . . .

and

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

Dividing (1) by

(2), \;{x^{2}}/{y^{2}}=\;{1}/{16}

\;{x}/{y}=\;{1}/{4}

i.e.

x=± \;{1}/{4} y

(± \;{1}/{4} y)^{2018} y^{2017}=\;{1}/{2}

y^{4035}=2^{4035}

y=2

Therefore,

x=± \;{1}/{4} y=± \;{1}/{2}

Hence,

x^{2}+y^{3}=\;{1}/{4}+8=\;{33}/{4}

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