AMC8 2013

AMC8 2013 · Q17

AMC8 2013 · Q17. It mainly tests Sequences & recursion (algebra), Averages (mean).

The sum of six consecutive positive integers is 2013. What is the largest of these six integers?

六个连续正整数的和是 2013。这些六个整数中最大的是多少？

(A) 335 335

(B) 338 338

(D) 345 345

(E) 350 350

Answer

Correct choice: (B)

正确答案：（B）

Solution

The arithmetic mean of these numbers is $\frac{\frac{2013}{3}}{2}=\frac{671}{2}=335.5$. Therefore the numbers are $333$, $334$, $335$, $336$, $337$, $338$, so the answer is $\boxed{\textbf{(B)}\ 338}$.

这些数的算术平均值为 $\frac{\frac{2013}{3}}{2}=\frac{671}{2}=335.5$。因此这些数是 $333$、$334$、$335$、$336$、$337$、$338$，答案是 $\boxed{\textbf{(B)}\ 338}$。

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