CAT 2023 Question Paper | Quant Slot 2

CAT Questions

CAT 2023 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 16 : If a certain amount of money is divided equally among \(n\) persons, each one receives Rs 352 . However, if two persons receive Rs 506 each and the remaining amount is divided equally among the other persons, each of them receive less than or equal to Rs 330 . Then, the maximum possible value of \(n\) is

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Video Explanation

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Explanatory Answer

“If a certain amount of money is divided equally among n persons, each one receives Rs 352 .”

Let the total amount be equal to T.
\( T = n \times 352 \)
“However, if two persons receive Rs 506 each and the remaining amount is divided equally among the other persons, each of them receive less than or equal to Rs 330”

\( T \leq 2 \times 506 + ( n - 2 ) \times 330 \)
\( n \times 352 \leq 2 \times 506 + ( n - 2 ) \times 330 \)
\( n \times 352 \leq 352 + n \times 330 \)
\( n \times 22 \leq 352 \)
\( n \leq \frac { 352 } { 22 } \)
\( n \leq 16 \)
So, the maximum value that n can take is 16.

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The question is " If a certain amount of money is divided equally among \(n\) persons, each one receives Rs 352 . However, if two persons receive Rs 506 each and the remaining amount is divided equally among the other persons, each of them receive less than or equal to Rs 330 . Then, the maximum possible value of \(n\) is "

The answer is '16'