CAT 2019 Question Paper | Quants Slot 1

CAT Questions

Exponents and Logarithms form an important part of the CAT syllabus. Logarithms require a  lot of practice as there is no intuitive way around them. The benefit of preparation is that there could be easy questions that can be attempted because of the preparation.

Question 26 : Let x and y be positive real numbers such that log₅(x + y) + log₅(x - y) = 3, and log₂y - log₂x = 1 - log₂3. Then xy equals

1. 25
2. 150
3. 250
4. 100

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Video Explanation

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Explanatory Answer

Given that, log₅(x + y) + log₅(x - y) = 3
We know log A + log B = log (A x B)
log₅(x + y) + log₅(x - y) = log₅(x² - y²)
log₅(x² - y²) = 3
x² - y² =
x² - y² = 125
Similarly, log₂y - log₂x = 1 - log₂3
log₂= log₂2 - log₂3
log₂= log₂
3y = 2x
(² - y² = 125
² - y² = 125
² = 125
² = 100
y = 10
x = 15
So, xy = 15 x 10 = 150

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The question is "Let x and y be positive real numbers such that log₅(x + y) + log₅(x - y) = 3, and log₂y - log₂x = 1 - log₂3. Then xy equals"

Hence, the answer is 150

Choice B is the correct answer.

 

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