If a and b are digits for which r 2a [-2pt] × b3 69 920 989 then a+b=

1997 AMC 12 Problem 1

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a

and

b

are digits for which

\begin{array}{r} 2a\\[-2pt] {}\times b3\\ \hline 69\\ 92\phantom0\\ \hline 989 \end{array}

then

a+b=

3

4

7

9

12

Use the first partial product to determine the two-digit top factor

The second partial product is the top factor multiplied by

b

The first partial product says

3(20+a)=69,

a=3.

The second says

23b=92,

b=4.

Thus

a+b=7,

and the correct answer is C.