Question

For $\{\begin{array}{c}|a+1|<3\\ |b-1|<10\end{array}$, if $x$ and $y$ are the greatest and the least integers respectively, satisfying $x<a+b<y$, then $x+y$ is

• A. $0$
• B. $26$
• C. $13$
• D. $-13$

Answer 1

The correct option is A $0$

$–3<a+1<3\Rightarrow -4<a<2...\left(1\right)-10<b-1<10\Rightarrow -9<b<11...\left(2\right)$

From eqns. $\left(1\right)$ and $\left(2\right)$,
$-4-9<a+b<2+11\Rightarrow -13<a+b<13$
$\therefore x=-13$ and $y=13$