Consider the following flowchart:

INPUT $\rightarrow$ Subtract $8 \rightarrow \square \rightarrow$ Divide by $2 \rightarrow \square \rightarrow$ Add $16 \rightarrow \square$ OUTPUT

If the OUTPUT is 32 , the INPUT must have been
(A) 16
(B) 28
(C) 36
(D) 40
(E) 32

## Part B: Each correct answer is worth 6.
Solution 1

We start from the OUTPUT and work back to the INPUT.

Since the OUTPUT 32 is obtained from adding 16 to the previous number, then the previous number is $32-16=16$.

$$
\text { INPUT } \rightarrow \text { Subtract } 8 \rightarrow \square \rightarrow \text { Divide by } 2 \rightarrow 16 \rightarrow \text { Add } 16 \rightarrow 32
$$

Since 16 is obtained by dividing the previous number by 2 , then the previous number is $2 \times 16$ or 32 .

$$
\text { INPUT } \rightarrow \text { Subtract } 8 \rightarrow 32 \rightarrow \text { Divide by } 2 \rightarrow 16 \rightarrow \text { Add } 16 \rightarrow 32
$$

Since 32 is obtained by subtracting 8 from the INPUT, then the INPUT must have been $32+8=40$.

$$
40 \rightarrow \text { Subtract } 8 \rightarrow 32 \rightarrow \text { Divide by } 2 \rightarrow 16 \rightarrow \text { Add } 16 \rightarrow 32
$$

## Solution 2

Suppose that the INPUT is $x$.

Subtracting 8 gives $x-8$.

Dividing this result by 2 gives $\frac{1}{2}(x-8)$ or $\frac{1}{2} x-4$.

Adding 16 to this result gives $\left(\frac{1}{2} x-4\right)+16=\frac{1}{2} x+12$, which is the OUTPUT.

$$
x \rightarrow \text { Subtract } 8 \rightarrow x-8 \rightarrow \text { Divide by } 2 \rightarrow \frac{1}{2} x-4 \rightarrow \text { Add } 16 \rightarrow \frac{1}{2} x+12
$$

If the OUTPUT is 32 , then $\frac{1}{2} x+12=32$ or $\frac{1}{2} x=20$ and so $x=40$.

Therefore, the INPUT must have been 40 .

ANSwER: (D)