Track / Stage 4 / 154 of 340 #414 of 1964

Problem 414

AMC 12 late, AIME early

Algebra Difficulty 4.7 Find the answer

Let set $A=\{2,0,1,8\}, B=\{2 a \mid a \in A\}$ , then the sum of all elements in $A \cup B$ is

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Answer: 31.
Solution: It is easy to know that $B=\{4,0,2,16\}$ , so $A \cup B=\{0,1,2,4,8,16\}$ . The sum of all elements in $A \cup B$ is $0+1+2+4+8+16=31$ .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.