CAT 2022 Linear and Quadratic Equations Question (Hard)

Question

Let and be natural numbers. If and , then equals

Accepted Answer

Step 1 We are given We need to find . Step 2 First equation Second equation Subtract the first from the second We know Thus Factor Therefore Since are natural numbers, can be 1, 2, 7, 14. Try Then But , so Try Then Try Then Impossible since , but b - a 142b a 1 1 Alternate approach Let s directly tr

CAT 2022

Quantitative

Linear and Quadratic Equations

Hard

Let $a$ and $b$ be natural numbers. If $a^2+a b+a=14$ and $b^2+a b+b=28$ , then $(2 a+b)$ equals

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