AMC8 1991

AMC8 1991 · Q12

AMC8 1991 · Q12. It mainly tests Linear equations, Fractions.

If $\frac{2 + 3 + 4}{3} = \frac{1990 + 1991 + 1992}{N}$, then $N =$

如果$\frac{2 + 3 + 4}{3} = \frac{1990 + 1991 + 1992}{N}$，则$N=$

(A) 3 3

(B) 6 6

(D) 1991 1991

(E) 1992 1992

Answer

Correct choice: (D)

正确答案：（D）

Solution

Any fraction of the form $((k-1) + k + (k+1)) / k$ equals 3, since $(k-1) + k + (k+1) = 3k$ and $3k / k = 3$. The denominator of the fraction must equal the middle term of the numerator. Thus $N = 1991$.

形如$((k-1) + k + (k+1)) / k$的分数等于3，因为$(k-1) + k + (k+1) = 3k$，$3k / k = 3$。分母必须等于分子中间项。因此$N = 1991$。

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