CAT 2024 Question Paper | Quant Slot 1

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 22 :If \(x\) is a positive real number such that \(4 \log _{10} x+4 \log _{100} x+8 \log _{1000} x=13\), then the greatest integer not exceeding \(x\), is

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Video Explanation

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Explanatory Answer

\[ \begin{array}{l} 4(\log x / \log 10)+4(\log x / 2 \log 10)+8(\log x / 3 \log 10)=13 \\ 4 \log x+2 \log x+(8 / 3) \log x=13 \\ \log x(4+2+8 / 3)=13 \\ (26 / 3) \log x=13 \\ \log x=3 / 2 \\ x=10^{1.5}=31.62 \end{array} \] The greater integer not exceeding \(x=31\)

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The question is "If \(x\) is a positive real number such that \(4 \log _{10} x+4 \log _{100} x+8 \log _{1000} x=13\), then the greatest integer not exceeding \(x\), is"

Hence, the answer is '31'

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