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CAT 2018 Question Paper | Quants Slot 1

CAT Previous Year Paper | CAT Exponents Questions | Question 25

This is a question from Logarithm and Exponents that appeared in CAT 2018 Question Paper. This topic is heavily tested in the CAT Exam. Among the topics under CAT Syllabus, Exponents and Logarithms is given more importance. A CAT aspirant's CAT online preparation is incomplete without mastering this topic. And the best way to captalize this is to solve questions from CAT Previous Year Paper.

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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