CAT 2022 Question Paper | Quant Slot 2

CAT 2022 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 14 : The number of distinct integer values of \(n\) satisfying \(\frac{4-\log _2 n}{3-\log _4 n}\lt0\), is

Video Explanation

Explanatory Answer

\( \frac { 4 - \log _ { 2 } ^ { n } } { 3 - \log _ { 4 } ^ { n } } < 0 \)
If \( \log _ { 2 } ^ { n } = 4 ; n = 2 ^ { 4 } = 16 \);
If \( \log _ { 4 } ^ { n } = 3 ; n = 4 ^ { 3 } = 64 \);
For any value of n < 16, the numerator is positive. For any value of n > 16, it is negative.
For any value of n < 64, the denominator is positive. For any value of n > 64, it is negative.
For a fraction to be negative, the numerator and the denominator must be of opposite signs.
In this case, n should be between 16 and 64.
The number of values that n can take = 63 - 16 = 47.

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

Hence, the answer is '47'

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