AMC8 2006

AMC8 2006 · Q24

AMC8 2006 · Q24. It mainly tests Base representation, Number theory misc.

In the multiplication problem below, A, B, C and D are different digits. What is A + B?

在下面的乘法问题中，A、B、C和D是不同的数字。A + B是多少？

(A) 1 1

(B) 2 2

(D) 4 4

(E) 9 9

Answer

Correct choice: (A)

正确答案：（A）

Solution

(A) We can decompose $CDCD$ into $CD \times 100 + CD = CD(101)$. That means that $A = 1$ and $B = 0$. The sum is $1 + 0 = 1$.

（A）我们可以将$CDCD$分解为$CD \times 100 + CD = CD(101)$。这意味着$A = 1$且$B = 0$。其和为$1 + 0 = 1$。

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