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Math·Advanced Math·Nonlinear functions

hard

$$f(x)=(x-a)(x-b)$$

The function $f$ is defined by the given equation, where $a$ and $b$ are integer constants. If $f(32)>0$, $f(35)<0$, and $f(38)>0$, which of the following could be the value of $a+b$?

A

35

B

37

C

67

D

69