The sum of the two 5 -digit numbers AMC10 and AMC12 is 123422. What is A + M + C?

2003 AMC 12A Problem 5

Attempt Problem 5 of the 2003 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2003 AMC 12A solutions, or check the answer key.

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The sum of the two

5

-digit numbers

\overline{AMC10}

and

\overline{AMC12}

123422.

What is

A + M + C?

10

11

12

13

14

\overline{AMC10}=100\cdot\overline{AMC}+10

The two numbers share the same leading three digits

\overline{AMC}

Write

\overline{AMC10}=100\cdot\overline{AMC}+10

and

\overline{AMC12}=100\cdot\overline{AMC}+12.

Their sum is

200\cdot\overline{AMC}+22=123422,

\overline{AMC}=617.

Then

A+M+C=6+1+7=14.

Thus, the correct answer is E.