AMC10 2003 A
AMC10 2003 A · Q11
AMC10 2003 A · Q11. It mainly tests Money / coins, Digit properties (sum of digits, divisibility tests).
The sum of the two 5-digit numbers AMC10 and AMC12 is 123422. What is A + M + C?
两个5位数 AMC10 和 AMC12 的和是 123422。A + M + C 的值是多少？
(A)
10
10
(B)
11
11
(C)
12
12
(D)
13
13
(E)
14
14
Answer
Correct choice: (E)
正确答案：（E）
Solution
(E) Since the last two digits of $AMC10$ and $AMC12$ sum to 22, we have
$AMC + AMC = 2(AMC) = 1234.$
Hence $AMC = 617$, so $A = 6$, $M = 1$, $C = 7$, and $A + M + C = 6 + 1 + 7 = 14$.
（E）由于 $AMC10$ 和 $AMC12$ 的后两位数字之和为 22，我们有
$AMC + AMC = 2(AMC) = 1234.$
因此 $AMC = 617$，所以 $A = 6$，$M = 1$，$C = 7$，并且 $A + M + C = 6 + 1 + 7 = 14$。
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