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Problem 74

Number theory Difficulty 1.2 Multiple choice CEMC Fermat · Canada · 2023

Ava’s machine takes four-digit positive integers as input. When
the four-digit integer $ABCD$ is
input, the machine outputs the integer $A\times B+C\times D$ . For example, when
the input is $1234$ , the output is
$1\times 2 + 3\times 4=2+12=14$ . When
the input is $2023$ , the output
is

Pick one

Official solution

Using the given rule, the output of the machine is $2 \times 0 + 2 \times 3 = 0 + 6 = 6$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.