1994 AJHSME Problems/Problem 23

Problem

If $X$ , $Y$ and $Z$ are different digits, then the largest possible $3-$ digit sum for

$\begin{tabular}{ccc} X & X & X \\ & Y & X \\ + & & X \\ \hline \end{tabular}$

has the form

$\text{(A)}\ XXY \qquad \text{(B)}\ XYZ \qquad \text{(C)}\ YYX \qquad \text{(D)}\ YYZ \qquad \text{(E)}\ ZZY$

Solution

The sum can be rewritten as $113X + 10Y$ . To get the largest possible sum, we maximize the hundreds digit, $X$ . If $X=9$ , the sum is a $4$ -digit number, so we let $X=8$ and $113(8)+10Y = 904+10Y$ . To continue maxmimizing this sum, we can let $Y=9$ , a different digit from $X$ , and $904+10(9)=994$ , which has the form $\boxed{\text{(D)}\ YYZ}$ .

1994 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 22	Followed by Problem 24
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
All AJHSME/AMC 8 Problems and Solutions

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1994 AJHSME Problems/Problem 23

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