If $A \# B$ denotes the average of $A$ and $B$, $A\$B$ denotes subtraction of $B$ from $A$, and $A\sim B$ denotes the remainder when $A$ is divided by $B$, then the value of $\{(3\#7)\#(7\sim3)\}\$(3\$7)$ is
A$1$
B$3$
C$5$
D$7$
Answer & Solution
Correct answer: D. $7$
First, $3\#7=(3+7)/2=5$. Next, $7\sim3$ is the remainder when 7 is divided by 3, which is 1. So $(3\#7)\#(7\sim3)=5\#1=(5+1)/2=3$. Also, $3\$7=3-7=-4$. Finally, $3\$(-4)=3-(-4)=7$.
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