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?

A. 26
B. 28
C. 30
D. 32
E. 34



Answer :

To find the missing fourth number in the group, follow these steps:

1. Determine the total sum of the four numbers:
- The average of the four numbers is given as 24.
- Since the average is the total sum divided by the number of elements, we can write:
[tex]\[ \text{Total Sum} = \text{Average} \times \text{Number of Elements} = 24 \times 4 = 96 \][/tex]

2. Calculate the sum of the first three numbers:
- The first three numbers are 35, 11, and 20.
- Adding them together:
[tex]\[ 35 + 11 + 20 = 66 \][/tex]

3. Find the remaining number by subtracting the sum of the first three numbers from the total sum:
- We have the total sum of all four numbers as 96.
- The sum of the first three numbers is 66.
- Therefore, the other number is:
[tex]\[ \text{Other Number} = \text{Total Sum} - \text{Sum of First Three Numbers} = 96 - 66 = 30 \][/tex]

Thus, the other number is 30.

So the correct answer is:
```
30
```