Question

$N$ 是一个大于 $9$ 且小于 $17$ 的数。下列哪个数可能是 $6$ 、 $10$ 和 $N$ 的平均数？

The number $N$ is between $9$ and $17.$ Which of the following could be the average of $6,$ $10,$ and $N?$

$8$

$10$

$12$

$14$

$16$

平均数是 $\frac{6 + 10 + N}{3}$ ；考察 $N$ 取值范围两端时的结果

The average is $\frac{6 + 10 + N}{3};$ find its value at each end of the range for $N$

当 $N$ 在 $9$ 和 $17$ 之间时，这个平均数在 $\frac{25}{3}$ 和 $11$ 之间

As $N$ runs from $9$ to $17,$ the average runs from $\frac{25}{3}$ to $11$

平均数为 $\frac{6 + 10 + N}{3} = \frac{16 + N}{3}$ 。当 $N = 9$ 时，这个式子为 $\frac{25}{3} \approx 8.3$ ；当 $N = 17$ 时，它等于 $11$ 。

所以平均数严格介于约 $8.3$ 和 $11$ 之间。选项中只有 $10$ 落在这个范围内。

所以正确答案是 B。

The average is $\frac{6 + 10 + N}{3} = \frac{16 + N}{3}.$ When $N = 9$ this is $\frac{25}{3} \approx 8.3,$ and when $N = 17$ it is $11.$

So the average lies strictly between about $8.3$ and $11.$ Among the choices, only $10$ falls in this range.

Thus, the correct answer is B .