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2023 CEMC Fermat Problems/Problem 5

Revision as of 22:14, 11 September 2025 by Anabel.disher (talk | contribs) (Created page with "==Problem== Ava's machine takes four-digit positive integers as input. When the four-digit integer <math>ABCD</math> is input, the machine outputs the integer <math>A \times...")
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Problem

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

$\text{ (A) }\ 0 \qquad\text{ (B) }\ 2 \qquad\text{ (C) }\ 3 \qquad\text{ (D) }\ 6 \qquad\text{ (E) }\ 8$

Solution

We have $A = 2$, $B = 0$, $C = 2$, and $D = 3$. Plugging this into the machine, we have:

$2 \times 0 + 2 \times 3 = 0 + 2 \times 3$

$=0 + 6$

$=\boxed {\textbf {(D) } 6}$

~anabel.disher

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