CAT 2023 Question Paper | Quant Slot 1

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 4 : Let \(n\) be the least positive integer such that 168 is a factor of \(1134^n\). If \(m\) is the least positive integer such that \(1134^n\) is a factor of \(168^m\), then \(m+n\) equals

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Video Explanation

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Explanatory Answer

The prime factorizations of 168 and 1134 are as follows:
168 = 2³ × 3 × 7
1134 = 2 × 3⁴ × 7
Clearly, the smallest positive integral value of n, such that 168 is a factor of 1134ⁿ is 3.
1134ⁿ = 1134³ = 2³ × 3¹² × 7³
Clearly, the smallest positive integral value of m, such that 1134³ is a factor of 168^m is 12.
Therefore, m + n = 12 + 3 = 15

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The question is " Let \(n\) be the least positive integer such that 168 is a factor of \(1134^n\). If \(m\) is the least positive integer such that \(1134^n\) is a factor of \(168^m\), then \(m+n\) equals "

Hence, the answer is '15'

Choice C is the correct answer.