Problem $3\mathrm{.}3$

In the US Interstate system, the numbering of an interstate gives you useful information about the

highway. Primary interstates have $1-$ or $2-$digit numbers $($that is$,$ between $1$ and $99).$ Odd$-$numbered

interstates run north$-$south, and even$-$numbered interstates run east$-$west. Three$-$digit interstates

$($numbered $>100)$ are auxiliary interstates, and the last two digits represent the primary interstate they

serve. If the hundreds digit is odd, then the interstate is a spur. If the hundreds digit is even, the

interstate is a bypass. For example, highway $I-110$ is a spur of $I-10,$ which itself runs east$-$west.

Do the following:

a$)$ Design a flowchart that would take an integer $($between $1-999)$ and display the appropriate

message out of the ones below, based on the rules given above.

i$.$ "The Interstate is a north$-$south primary interstate."

ii$.$ "The Interstate is an east$-$west primary interstate."

iii. "The Interstate is a spur of the primary interstate:

##${?}^{\text{'}\text{'}}$

iv$.$ "The Interstate is a bypass of the primary interstate:

##$"$

b$)$ Come up with the mathematical expressions you might need to answer the questions in your

flowchart.

Hint: Calculate the expression xMOD$2$ for several even and odd values of $x.$