CAT 2022 Question Paper | Quant Slot 1

CAT Questions

CAT 2022 Quant was dominated by Arithmetic followed by Algebra. 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 12 : For any real number \(x\), let \([x]\) be the largest integer less than or equal to \(x\). If \(\sum_{n=1}^N\left[\frac{1}{5}+\frac{n}{25}\right]=25\) then \(N\) is

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Video Explanation

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Explanatory Answer

\( [ \frac { 1 } { 5 } + \frac { n } { 25 } ] = [ \frac { n + 5 } { 25 } ] \)

Range of n	Count of n	Value of \( [ \frac { n + 5 } { 25 } ] \)
1 to 19	19	0
20 to 44	25	1
45 to 69	25	2
…		…

Clearly when N = 44, we see that \(\sum_{n=1}^N\left[\frac{1}{5}+\frac{n}{25}\right]=19(0)+25(1)=25\).
Therefore, N = 44.

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The question is " For any real number \(x\), let \([x]\) be the largest integer less than or equal to \(x\). If \(\sum_{n=1}^N\left[\frac{1}{5}+\frac{n}{25}\right]=25\) then \(N\) is "

Hence, the answer is '44'