1990 AJHSME Problems/Problem 1

From AoPSWiki

Problem

What is the smallest sum of two $3$ -digit numbers that can be obtained by placing each of the six digits $4,5,6,7,8,9$ in one of the six boxes in this addition problem?

$\text{(A)}\ 947 \qquad \text{(B)}\ 1037 \qquad \text{(C)}\ 1047 \qquad \text{(D)}\ 1056 \qquad \text{(E)}\ 1245$

Solution

Let the two three-digit numbers be $\overline{abc}$ and $\overline{def}$ . Their sum is equal to $100(a+d)+10(b+e)+(c+f)$ .

To minimize this, we need to minimize the contribution of the $100$ factor, so we let $a=4$ and $d=5$ . Similarly, we let $b=6$ , $e=7$ , and then $c=8$ and $f=9$ . The sum is $100(9)+10(13)+(17)=1047 \rightarrow \boxed{\text{C}}$

1990 AJHSME (Problems • Resources)
Preceded by First Problem	Followed by Problem 2
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25

Personal tools

Navigation

Search

Toolbox

1990 AJHSME Problems/Problem 1

From AoPSWiki

Problem

Solution

See Also