The digits $2,3,5,7$, and 8 can be used, each exactly once, to form many five-digit integers. Of these integers, $N$ is the one that is as close as possible to 30000 . What is the tens digit of $N$ ?
(A) 2
(B) 5
(C) 3
(D) 8
(E) 7

Part B: Each correct answer is worth 6.
We find the smallest such integer greater than 30000 and the largest such integer less than 30000 and then determine which is closest to 30000 .

Let $M$ be the smallest integer greater than 30000 that is formed using the digits 2, 3, 5, 7, and 8 , each exactly once.

Since $M$ is greater than 30000 , its ten thousands digit is at least 3 .

To make $M$ as small as possible (but greater than 30000 ), we set its ten thousands digit to 3 . To make $M$ as small as possible, its thousands digit should be as small as possible, and thus equals 2.

Continuing in this way, its hundreds, tens and ones digits are 578. Thus, $M=32578$.

Let $m$ be the largest integer less than 30000 that is formed using the digits $2,3,5,7$, and 8 , each exactly once.

Since $m$ is less than 30000 , its ten thousands digit is less than 3 and must thus be 2 .

To make $m$ as large as possible (but less than 30000 ), its thousands digit should be as large as possible, and thus equals 8 .

Continuing in this way, its hundreds, tens and ones digits are 7,5 and 3, respectively. Thus, $m=28753$.

Since $M-30000=2578$ and $30000-m=1247$, then $m$ is closer to 30000 .

Thus, $N=m=28753$. The tens digit of $N$ is 5 .

ANswer: (B)