CAT 2022 Slot 1 QA Question 10: Let $a$ and $b$ be natural numbers. If $a^2 + ab + a = 14$ and $b^2 + ab + b = 28$, then $(2a + b)$ equals

Question

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

Accepted Answer

$a^2 + ab + a = a(a+b+1) = 14$
$b^2 + ab + b = b(a+b+1) = 28$
Dividing the two equations,
$\dfrac{a}{b} = \dfrac{14}{28} = \dfrac{1}{2}$
$\Rightarrow b = 2a$
$a(a+b+1) = 14$
$\Rightarrow a(3a+1) = 14$
$\Rightarrow 3a^2 + a - 14 = 0$
$\Rightarrow (3a+7)(a-2) = 0$
$\Rightarrow a = 2$
$\Rightarrow b =

Let aaa and bbb be natural numbers. If a2+ab+a=14a^2 + ab + a = 14a2+ab+a=14 and b2+ab+b=28b^2 + ab + b = 28b2+ab+b=28, then (2a+b)(2a + b)(2a+b) equals

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