AMC8 2022

AMC8 2022 · Q16

AMC8 2022 · Q16. It mainly tests Averages (mean), Arithmetic misc.

Four numbers are written in a row. The average of the first two is $21,$ the average of the middle two is $26,$ and the average of the last two is $30.$ What is the average of the first and last of the numbers?

四个数字排成一行。前两个数的平均数是$21$，中间两个数的平均数是$26$，后两个数的平均数是$30$。这四个数的第一个和最后一个的平均数是多少？

(A) 24 24

(B) 25 25

(D) 27 27

(E) 28 28

Answer

Correct choice: (B)

正确答案：（B）

Solution

Note that the sum of the first two numbers is $21\cdot2=42,$ the sum of the middle two numbers is $26\cdot2=52,$ and the sum of the last two numbers is $30\cdot2=60.$ It follows that the sum of the four numbers is $42+60=102,$ so the sum of the first and last numbers is $102-52=50.$ Therefore, the average of the first and last numbers is $50\div2=\boxed{\textbf{(B) } 25}.$

注意前两个数的和是$21\cdot2=42$，中间两个数的和是$26\cdot2=52$，后两个数的和是$30\cdot2=60$。由此，四数的总和是$42+60=102$，所以第一个和最后一个数的和是$102-52=50$。因此，第一个和最后一个数的平均数是$50\div2=\boxed{\textbf{(B) } 25}$。

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