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 6 If \(10^{68}\) is divided by 13 , the remainder is

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Video Explanation

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Explanatory Answer

\[ \begin{array}{lll} \operatorname{Re}\left[\frac{10^1}{13}\right]=10 ; & \operatorname{Re}\left[\frac{10^2}{13}\right]=9 ; & \operatorname{Re}\left[\frac{10^3}{13}\right]=12 ; \\ \operatorname{Re}\left[\frac{10^4}{13}\right]=3 ; & \operatorname{Re}\left[\frac{10^5}{13}\right]=4 ; & \operatorname{Re}\left[\frac{10^6}{13}\right]=1 \end{array} \] So, after every power of 6, the remainder repeats its patterns.
Hence, \[ \begin{array}{l} \operatorname{Re}\left[\frac{10^{66}}{13}\right]=1 \\ \operatorname{Re}\left[\frac{10^{67}}{13}\right]=10 \\ \operatorname{Re}\left[\frac{10^{68}}{13}\right]=9 \end{array} \]

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The question is "If \(10^{68}\) is divided by 13 , the remainder is "

Hence, the answer is '9'

Choice B is the correct answer.

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