AMC8 1994

AMC8 1994 · Q25

AMC8 1994 · Q25. It mainly tests Fractions, Digit properties (sum of digits, divisibility tests).

Find the sum of the digits in the answer to $\frac{9999...99}{94 \text{ nines}} \times \frac{4444...44}{94 \text{ fours}}$ where a string of 94 nines is multiplied by a string of 94 fours.

求 $\frac{9999...99}{94 \text{ nines}} \times \frac{4444...44}{94 \text{ fours}}$ 的答案中各位数字之和，其中94个9的串乘以94个4的串。

(A) 846 846

(B) 855 855

(D) 954 954

(E) 1072 1072

Answer

Correct choice: (A)

正确答案：（A）

Solution

Product is 444...4 (93 fours) 3 555…5 (93 fives) 6. Digit sum 93×4 +3 +93×5 +6 =93×9 +9=846.

积是444...4（93个4）3 555…5（93个5）6。各位数字和93×4 +3 +93×5 +6 =93×9 +9=846。

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