AMC8 2025

AMC8 2025 · Q14

AMC8 2025 · Q14. It mainly tests Linear equations, Averages (mean).

A number $N$ is inserted into the list $2$, $6$, $7$, $7$, $28$. The mean is now twice as great as the median. What is $N$?

一个数$N$插入列表$2$、$6$、$7$、$7$、$28$中。现在平均数是中位数的两倍。$N$是多少？

(A) \ 7 \ 7

(B) \ 14 \ 14

(D) \ 28 \ 28

(E) \ 34 \ 34

Answer

Correct choice: (E)

正确答案：（E）

Solution

The median of the list is $7$, so the mean of the new list will be $7 \cdot 2 = 14$. Since there are $6$ numbers in the new list, the sum of the $6$ numbers will be $14 \cdot 6 = 84$. Therefore, $2+6+7+7+28+N = 84 \implies N = \boxed{\text{(E) 34}}$

列表的中位数是$7$，所以新列表的平均数是$7 \cdot 2 = 14$。新列表有$6$个数，$6$个数的和是$14 \cdot 6 = 84$。因此，$2+6+7+7+28+N = 84 \implies N = \boxed{\text{(E) 34}}$

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