The average of 3 numbers is 7 and average of first two numbers is 4. What is the third number ?

Options

A. 15
B. 13
C. 7
D. 4

Answer

To find the third number given the average of three numbers and the average of the first two numbers, we can follow these steps:

### Step 1: Understand the average formula
The average (mean) of a set of numbers is calculated using the formula:
\[ \text{Average} = \frac{\text{Sum of all observations}}{\text{Number of observations}} \]

### Step 2: Calculate the sum of the three numbers
We know that the average of three numbers is 7. Therefore, we can set up the equation:
\[ \text{Average} = \frac{\text{Sum of three numbers}}{3} \]
Substituting the given average:
\[ 7 = \frac{\text{Sum of three numbers}}{3} \]
To find the sum of the three numbers, we multiply both sides by 3:
\[ \text{Sum of three numbers} = 7 \times 3 = 21 \]

### Step 3: Calculate the sum of the first two numbers
Next, we know that the average of the first two numbers is 4. Using the same average formula:
\[ \text{Average} = \frac{\text{Sum of first two numbers}}{2} \]
Substituting the given average:
\[ 4 = \frac{\text{Sum of first two numbers}}{2} \]
To find the sum of the first two numbers, we multiply both sides by 2:
\[ \text{Sum of first two numbers} = 4 \times 2 = 8 \]

### Step 4: Find the third number
Now, we can find the third number by subtracting the sum of the first two numbers from the sum of all three numbers:
\[ \text{Third number} = \text{Sum of three numbers} - \text{Sum of first two numbers} \]
Substituting the values we calculated:
\[ \text{Third number} = 21 - 8 = 13 \]

### Final Answer
The third number is **13**.

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