CAT 2018 Question Paper | Quants Slot 1

CAT Questions

This olympiad-style problem is a wonderful question which is based on Number Theory. Historically, CAT Previous Year paper are known for rolling out at least one or two questions based on this topic. Solve this question to boost your confidence to crack the Quantitative Aptitude section of the CAT Question Paper.

Question 21 :The number of integers x such that 0.25 < 2^x < 200, and 2^x + 2 is perfectly divisible by either 3 or 4, is [TITA]

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Number Theory

Given 0.25 ≤ 2x
0.25 = \\frac{1}{4}) =(\\frac{1}{2}))² = 2^-2
Similarly, 2⁶ = 64, 2⁷ = 128, 2⁸ > 200
Substituting the values and checking for divisibility
Number of Integers x = 5

The question is "The number of integers x such that 0.25 < 2^x < 200, and 2^x + 2 is perfectly divisible by either 3 or 4, is [TITA]"

Hence, the answer is 5 integers

 

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