Question

a group of four numbers has an average (arithmetic mean) of 24. the first three numbers are 35, 11, and 20. what is the other number?
26
28
30
32
34

Explanation:

Step1: Find the sum of the four - number group

The formula for the arithmetic mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Given $n = 4$ and $\bar{x}=24$, the sum of the four - number group is $S_4=n\times\bar{x}=4\times24 = 96$.

Step2: Find the sum of the first three numbers

The first three numbers are 35, 11, and 20. Their sum is $S_3=35 + 11+20=66$.

Step3: Find the fourth number

Let the fourth number be $x$. We know that $S_4=S_3 + x$. So $x=S_4 - S_3$. Substituting the values of $S_4$ and $S_3$, we get $x=96 - 66=30$.

Answer:

C. 30