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 14 :Suppose \(x_1, x_2, x_3, \ldots, x_{100}\) are in arithmetic progression such that \(x_5=-4\) and \(2 x_6+2 x_9=x_{11}+x_{13}\). Then, \(x_{100}\) equals

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Video Explanation

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Explanatory Answer

\[ \begin{array}{l} 2 x_6+2 x_9=x_{11}+x_{13} . \\ 2 x_6+2 x_9=2 x_{12} \\ x_6+x_9=x_{12} \\ \text { Since } x_5=-4 \\ -4+d+-4+4 d=-4+7 d \\ 2 d=-4 \\ d=-2 \\ x_4=-2 \\ x_3=-0 \\ x_2=2 \\ x_1=4 \end{array} \] Now \(x_{100}=x_1+99 d=4+(-2)(99)=4-198=-194\)

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The question is "Suppose \(x_1, x_2, x_3, \ldots, x_{100}\) are in arithmetic progression such that \(x_5=-4\) and \(2 x_6+2 x_9=x_{11}+x_{13}\). Then, \(x_{100}\) equals"

Hence, the answer is '-194'

Choice B is the correct answer.

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