CAT 2022 Slot 1 QA Question & Solution
AlgebraEasy
Question
Let a and b be natural numbers. If $a^2 + ab + a = 14$ and $b^2 + ab + b = 28$, then $(2a + b)$ equals
Options
8
7
10
9
Solution
a(a + b + 1) = 14 ...... (1)
b(a + b + 1) = 28 ...... (2)
$\frac{a}{b}=\frac{1}{2}$
b = 2a
Substituting in (1), we get
a(3a + 1) = 14
$3a^2+a-14=0$
$3a^2-6a+7a-14=0$
$3a\left(a-2\right)+7\left(a-2\right)=0$
Given, a and b are natural numbers.
Therefore, a = 2 and b = 4
2a + b = 2(2) + 4 = 8
The answer is option A.