CAT 2023 Number System Question (Hard)

Question

For any natural numbers , , and , such that divides both and , must be a common divisor of

Accepted Answer

Step 1 We are given We want to eliminate or to find a useful expression. Step 2 Form a linear combination to eliminate Multiply first equation by 3 Now subtract second equation So Step 3 Now eliminate Multiply first equation by 3 Compare with Subtract same result Now eliminate another way Let s try

CAT 2023

Quantitative

Number System

Hard

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

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