AMC8 1994

AMC8 1994 · Q6

AMC8 1994 · Q6. It mainly tests Parity (odd/even), Digit properties (sum of digits, divisibility tests).

The unit's digit (one's digit) of the product of any six consecutive positive whole numbers is

任意六个连续正整数的乘积的个位数（个位）是

(A) 0 0

(B) 2 2

(D) 6 6

(E) 8 8

Answer

Correct choice: (A)

正确答案：（A）

Solution

Any selection of six consecutive positive whole numbers has at least one multiple of 5 and at least one multiple of 2. Thus, the product has at least one factor of 5 × 2 = 10 and must end in 0.

任意六个连续正整数中至少有一个5的倍数和至少有一个2的倍数。因此，该乘积至少有一个因子 $5 \times 2 = 10$，一定以0结尾。

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