The average of five numbers is 371.8. The average of the first and second numbers is 256.5 and the average of the fourth and fifth numbers is 508. Which of the following is the third number?

Options

A. 360
B. 310
C. 380
D. 330

Answer

To find the third number, we can follow these steps:

1. **Calculate the total sum of the five numbers.**
The average of five numbers is given as 371.8. Therefore, the total sum of the five numbers can be calculated using the formula:
\[ \text{Total Sum} = \text{Average} \times \text{Number of Items} \]
\[ \text{Total Sum} = 371.8 \times 5 = 1859 \]

2. **Calculate the sum of the first and second numbers.**
The average of the first and second numbers is given as 256.5. Thus, the sum of the first and second numbers is:
\[ \text{Sum of 1st and 2nd} = \text{Average} \times \text{Number of Items} \]
\[ \text{Sum of 1st and 2nd} = 256.5 \times 2 = 513 \]

3. **Calculate the sum of the fourth and fifth numbers.**
The average of the fourth and fifth numbers is given as 508. Therefore, the sum of the fourth and fifth numbers is:
\[ \text{Sum of 4th and 5th} = \text{Average} \times \text{Number of Items} \]
\[ \text{Sum of 4th and 5th} = 508 \times 2 = 1016 \]

4. **Set up the equation to find the third number.**
We know that the total sum of the five numbers is the sum of the first and second numbers, the third number, and the sum of the fourth and fifth numbers:
\[ \text{Total Sum} = \text{Sum of 1st and 2nd} + \text{3rd Number} + \text{Sum of 4th and 5th} \]
Plugging in the values we calculated:
\[ 1859 = 513 + \text{3rd Number} + 1016 \]

5. **Solve for the third number.**
Combine the known sums:
\[ 1859 = 1529 + \text{3rd Number} \]
Now, isolate the third number:
\[ \text{3rd Number} = 1859 - 1529 = 330 \]

Thus, the third number is **330**.