If $c$ and $d$ are two integers and $@$ is defined in $a$ and $b$ as $@(a,b)=(a+1)(b+2)$, and $@(c,d)$ equals the product of $3$ and $5$, then what could be the value of $c+d$?
A. $-11$
B. $0$
C. $5$
D. $6$
E. $11
I don't understand the question here. Can $@(a,b)=@(c,d)$?
$$ @(c,d) = (c+1)\cdot (d+2) = 3\cdot 5 $$
So you have, $$c+1 = 3 \text{ and } d+2=5$$ or $$c+1 = -3 \text{ and } d+2 = -5$$
In the first solution, you get $c+d = 2+3 = 5$.
In the second solution, you get $$ c+d = -4 + -7 = -11 $$ So $C,A$ are correct.