# CAT 2023 Question Paper | Quant Slot 2

###### CAT Previous Year Paper | CAT Quant Questions | Question 3

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 3 : For any natural numbers $m, n$, and $k$, such that $k$ divides both $m+2 n$ and $3 m+4 n, k$ must be a common divisor of

1. $2 m$ and $3 n$
2. $m$ and $2 n$
3. $2 m$ and $n$
4. $m$ and $n$

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k divides m + 2n
So, k also divides 2(m + 2n) = 2m + 4n
It is given that k divides 3m + 4n
Which means, k should also divide (3m + 4n) – (2m + 4n)
∴k divides m
Since k divides m and m + 2n
k should also divide (m + 2n) – m = 2n
Therefore, k divides m and 2n.

The question is " For any natural numbers $m, n$, and $k$, such that $k$ divides both $m+2 n$ and $3 m+4 n, k$ must be a common divisor of "

##### Hence, the answer is '$m$ and $2 n$'

Choice B is the correct answer.

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