CAT 2022 Slot 2 QA Q14 Logarithms & Exponents

Question 14 of the Quantitative Ability (QA) section, CAT 2022 Slot 2, with CAT's official answer and a worked solution.

The number of distinct integer values of \(n\) satisfying \(\frac{4-\log _2 n}{3-\log _4 n}\lt0\), is

TITA: type in the answer. There are no options and no negative marking.

Answer: 47 Logarithms & Exponents TITA

Solution

Let \(t=\log_2n\), so \(\log_4n=t/2\). The expression is \(\frac{2(4-t)}{6-t}<0\).
This holds for \(4<t<6\), i.e. \(16<n<64\).
Integers 17 to 63: 47 values.