AMC8 2017

AMC8 2017 · Q5

AMC8 2017 · Q5. It mainly tests Fractions, Basic counting (rules of product/sum).

What is the value of the expression $\frac{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8}{1 + 2 + 3 + 4 + 5 + 6 + 7 + 8}$?

求表达式 $\frac{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8}{1 + 2 + 3 + 4 + 5 + 6 + 7 + 8}$ 的值？

(A) 1020 1020

(B) 1120 1120

(D) 2240 2240

(E) 3360 3360

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): The sum $1 + 2 + 3 + \cdots + 8 = 36$, so the desired quotient is \[\frac{1\cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8}{36} = 4 \cdot 5 \cdot 7 \cdot 8 = 1120.\]

答案 (B)：$1+2+3+\cdots+8=36$，因此所求的商为 \[\frac{1\cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8}{36} = 4 \cdot 5 \cdot 7 \cdot 8 = 1120.\]

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