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Question 25 :Given that x2018 y2017 = 1/2 and x2016 y2019 = 8, the value of x2 + y3 is

  1. \\frac{37}{4})
  2. \\frac{31}{4})
  3. \\frac{35}{4})
  4. \\frac{33}{4})

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Explanatory Answer

Method of solving this CAT Question from Exponents

x2018 y2017 = \\frac{1}{2}) ---(1)
x2016 y2019 = 8 ---(2)
Divide (1) by (2) we get (\\frac{x}{y}))2 = \\frac{1}{16})
y = 4x
Substituting the value of y in (2)
x2016 . x2019 . 42019 = 23
x4035 . 24038 = 23
x4035 = 2-4035 => x = \\frac{1}{2}) y = 2
x2 + y3 = \\frac{33}{4})

The question is "Given that x2018 y2017 = 1/2 and x2016 y2019 = 8, the value of x2 + y3 is"

Hence, the answer is \\frac{33}{4})

Choice D is the correct answer.


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