Track / Stage 4 / 333 of 340 #593 of 1964

Problem 593

AMC 12 late, AIME early

Number theory Difficulty 5.0 Find the answer

5. (3 points) Three-digit even numbers $A, B, C, D, E$ satisfy $A<B<C<D<E$ . If $A+B+C+D+E=4306$ , then $A$ is the smallest. $\qquad$

Your answer

A number or a short expression. Spacing, $ signs and \frac vs / are all fine.

Official solution

【Solution】Solution: The largest three-digit even number is 998,
To satisfy $A$ being the smallest and $A<B<C<D<E$ , then $E$ is at most 998, $D$ is at most 996, $C$ is at most 994, and $B$ is at most 992,
$\begin{array}{l} 4306-(998+996+994+992) \\ =4306-3980 \\ =326, \end{array}$

Therefore, $A$ is at least 326. The answer is: 326.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.