CAT 2024 Question Paper | Quant Slot 3

CAT Questions

CAT 2024 Quant was dominated by Algebra followed by Arithmetic. 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 16 If \(3^a=4,4^b=5,5^c=6,6^d=7,7^e=8\) and \(8^f=9\), then the value of the product abcdef is

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Video Explanation

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Explanatory Answer

\[ \begin{array}{l} 3^a=4 \Rightarrow \log _3 4=a \\ \Rightarrow \frac{\log 4}{\log 3}=a \end{array} \] Similarly, \[ \begin{array}{l} \frac{\log 5}{\log 4}=b ; \quad \frac{\log 6}{\log 5}=c ; \quad \frac{\log 7}{\log 6}=d ; \frac{\log 8}{\log 7}=e ; \frac{\log 9}{\log 8}=f \\

a b c d e f=\frac{\log 4}{\log 3} \times \frac{\log 5}{\log 4} \times \frac{\log 6}{\log 5} \times \frac{\log 7}{\log 6} \times \frac{\log 8}{\log 7} \times \frac{\log 9}{\log 8} \\

\text { abcdef }=\frac{\log 9}{\log 3}=2 \end{array} \]

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The question is "If \(3^a=4,4^b=5,5^c=6,6^d=7,7^e=8\) and \(8^f=9\), then the value of the product abcdef is"

Hence, the answer is '2'

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