1996 AHSME Problems/Problem 1

Problem

The addition below is incorrect. What is the largest digit that can be changed to make the addition correct?

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$\text{(A)}\ 4\qquad\text{(B)}\ 5\qquad\text{(C)}\ 6\qquad\text{(D)}\ 7\qquad\text{(E)}\ 8$

Solution

Doing the addition as is, we get $641 + 852 + 973 = 2466$ . This number is $10$ larger than the desired sum of $2456$ . Therefore, we must make one of the three numbers $10$ smaller.

We may either change $641 \rightarrow 631$ , $852 \rightarrow 842$ , or $973 \rightarrow 963$ . Either change results in a valid sum. The largest digit that could be changed is thus the $7$ in the number $973$ , and the answer is $\boxed{D}$ .

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1996 AHSME Problems/Problem 1

Problem

Solution