CAT 2018 Question Paper | Quants Slot 1

CAT Questions

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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Video Explanation

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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.