If a, b, and c are digits for which r 7a2 -48b c73 then a+b+c=

1998 AMC 12 Problem 3

Attempt Problem 3 of the 1998 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1998 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

a,

b,

and

c

are digits for which

\begin{array}{r} 7a2\\ {}-48b\\ \hline c73 \end{array}

then

a+b+c=

14

15

16

17

18

The units column must borrow from the tens column

Continue the borrowing through the tens and hundreds columns

The units column gives

12-b=3,

b=9.

In the tens column,

a-1

must borrow, and

a-1+10-8=7,

giving

a=6.

The hundreds column then gives

7-1-4=c=2.

Therefore

a+b+c=6+9+2=17,

so D is correct.