# CAT 2023 Question Paper | Quant Slot 1

###### CAT Previous Year Paper | CAT Quant Questions | Question 4

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

1. 12
2. 9
3. 15
4. 24

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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 168m is 12.
Therefore, m + n = 12 + 3 = 15

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.

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