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 18 :For any natural number \(n\), let \(a_n\) be the largest integer not exceeding \(\sqrt{n}\). Then the value of \(a_1+a_2+\cdots+a_{50}\) is

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Video Explanation

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Explanatory Answer

Largest integer not exceeding \(\sqrt{ }\) n for \(a_1, a_2, a_3=1\)
Largest integer not exceeding \(\sqrt{ }\) n for \(a_4, a_5, a_6, a_7, a_8=2\)
Largest integer not exceeding \(\sqrt{ }\) n for \(a_{49}=7\)
\[ \begin{array}{l} a_1 \text { to } a_3=3 * 1=3 \\ a_4 \text { to } a_8=5 * 2=10 \\ a_9 \text { to } a_{15}=7 * 3=21 \\ a_{16} \text { to } a_{24}=9 * 4=36 \\ a_{25} \text { to } a_{35}=11 * 5=55 \\ a_{36} \text { to } a_{48}=13 * 6=78 \\ a_{49}=7 \\ a_{50}=7 \\ a_1+a_2+\cdots+a_{50}=3+10+21+36+55+78+7+7=217 \end{array} \]

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The question is "For any natural number \(n\), let \(a_n\) be the largest integer not exceeding \(\sqrt{n}\). Then the value of \(a_1+a_2+\cdots+a_{50}\) is"

Hence, the answer is '217'

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