CAT 2021 Question Paper | Quant Slot 3

CAT 2021 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 6 : For a real number a, if \(\frac{\log _{15} a+\log _{32} a}{\left(\log _{15} a\right)\left(\log _{32} a\right)}=\) = 4 then a must lie in the range

Video Explanation

Explanatory Answer

\( \frac { \log _ { 15 } ^ { a } + \log _ { 32 } ^ { a } } { \left( \log _ { 15 } ^ { a } \times \log _ { 32 } ^ { a } \right) } \) = 4
\( \frac { 1 } { \log _ { 32 } ^ { a } } + \frac { 1 } { \log _ { 15 } ^ { a } } \)= 4
\( \log _ { a } ^ { 32 } + \log _ { a } ^ { 15 } \)= 4
\( \log _ { a } ^ { ( 32 \times 15 ) } \) = 4
a⁴ = 32 × 15 = 480
We know that, 4⁴ = 256 and 5⁴ = 625
256 < 480 < 625
4⁴ < a⁴ < 5⁴
4 < a < 5

The question is " For a real number a, if \(\frac{\log _{15} a+\log _{32} a}{\left(\log _{15} a\right)\left(\log _{32} a\right)}=\) = 4 then a must lie in the range "

Hence, the answer is '4 < a < 5'

Choice A is the correct answer.

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