An integer $n$ is decreased by 2 and then multiplied by 5 . If the result is 85 , the value of $n$ is
(A) 17
(B) 19
(C) 21
(D) 23
(E) 25
Solution 1

We undo each of the operations in reverse order.

The final result, 85, was obtained by multiplying a number by 5 . This number was $85 \div 5=17$. The number 17 was obtained by decreasing $n$ by 2 . Thus, $n=17+2=19$.

## Solution 2

When $n$ is decreased by 2 , we obtain $n-2$.

When $n-2$ is multiplied by 5 , we obtain $5 \times(n-2)$.

From the given information, $5 \times(n-2)=85$ which means that $5 n-10=85$.

From this, we obtain $5 n=95$ and so $n=\frac{95}{5}=19$.

ANSWER: (B)