1995 AMC 12 Problem 13

Question

The addition below is incorrect. The display can be made correct by changing one digit

d,

wherever it occurs, to another digit

e.

Find the sum of

d

and

e.

\begin{array}{rrrrrrr}&7&4&2&5&8&6\\+&8&2&9&4&3&0\\\hline1&2&1&2&0&1&6\end{array}

4

6

8

10

more than

10

Add from right to left and track each carry

Remember that the same replacement must be made at every occurrence of

d

The units, tens, and hundreds columns work with carries

0,

1,

1.

In the thousands column, replacing every

2

by

6

gives

6+9+1=16,

so the result digit is also

6.

The next columns then give

4+6+1=11

and

7+8+1=16,

producing the corrected equation

746586+869430=1616016.

Thus

d+e=2+6=8,

and the correct answer is C.

Problem 13 in other years