CAT 2020 Slot 2 QA Question 17: If $x$ and $y$ are non-negative integers such that $x + 9 = z$, $y + 1 = z$ and $x + y

Question

If $x$ and $y$ are non-negative integers such that $x + 9 = z$, $y + 1 = z$ and $x + y < z + 5$, then the maximum possible value of $2x + y$ equals

Accepted Answer

From the first two equations,

$x = z - 9$
$y = z - 1$

Substitute these into the inequality.
$x + y 
$z - 9 + z - 1 
$z

Since $x$ and $y$ are non-negative integers, $z$ is an integer and $z \geq 9$. The maximum possible $z$ is $14$.

$x = 14 - 9 = 5$
$y = 14 - 1 = 13$
$2x + y = 2 	imes 5 + 13 =

If xxx and yyy are non-negative integers such that x+9=zx + 9 = zx+9=z, y+1=zy + 1 = zy+1=z and x+y<z+5x + y < z + 5x+y<z+5, then the maximum possible value of 2x+y2x + y2x+y equals