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CAT 2018 Question Paper | Quants Slot 2

CAT Previous Year Paper | CAT Number theory and Inequalities Questions | Question 13

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Here's a question from CAT Previous Year Papers 2018 that appears simple, but requires a strong predisposition for math! If you can prove your metal by eliminating the wrong options from this CAT 2018 Question Paper problem, then you are through! Try your hands on this beauty from Inequalities and then go on to have a look at how Rajesh solves it.

Question 13 : The smallest integer n for which 4ⁿ ＞ 17¹⁹ holds, is closest to

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Explanatory Answer

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Explanatory Answer

Method of solving this CAT Question from Number theory and Inequalities

Given that 4ⁿ > 17¹⁹
The smallest integer n for which 4ⁿ > 17¹⁹ holds has to be found 4ⁿ > 17¹⁹ can be also written as (4²)^{\\frac{n}{2})} > 17¹⁹
16^{\\frac{n}{2})} > 17¹⁹
We can assume n = 19, 16¹⁹ cannot be greater than 17¹⁹
16^{\\frac{38}{2})} cannot be greater than 17¹⁹ so n cannot be 38
And similarly n cannot be less than 38 so we can eliminate the options less than 38 and so the only possible value n could take is 39