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 10 :When \(10^{100}\) is divided by 7 , the remainder is

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Video Explanation

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Explanatory Answer

\[ \begin{array}{l} \operatorname{Rem}(10 / 7)=3 \\ \operatorname{Rem}\left(10^{100} / 7\right)=\operatorname{Rem}\left(3^{100} / 7\right) \\ \operatorname{Rem}(3 / 7)=3 \\ \operatorname{Rem}\left(3^2 / 7\right)=2 \\ \operatorname{Rem}\left(3^3 / 7\right)=6 \\ \operatorname{Rem}\left(3^4 / 7\right)=4 \\ \operatorname{Rem}\left(3^5 / 7\right)=5 \\ \operatorname{Rem}\left(3^6 / 7\right)=1 \\ \operatorname{Rem}\left(3^{100} / 7\right)=\left\{\operatorname{Rem}\left(3^6 / 7\right)\right\}^{16} * \operatorname{Rem}\left(3^4 / 7\right)=1^{16 *} 4=4 \end{array} \] The answer is 4 .

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The question is "When \(10^{100}\) is divided by 7 , the remainder is "

Hence, the answer is '4'

Choice D is the correct answer.

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