The average of six numbers is 44.
The average of two of those numbers is 11.
`{:("Quantity A","Quantity B"),("The average of the other",77),("4 numbers",):}`

Options

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the infromation given.

Answer

To solve the problem step by step, we will follow the information given and perform the necessary calculations.

### Step 1: Calculate the sum of the six numbers.
The average of six numbers is given as 44. The formula for average is:

\[ \text{Average} = \frac{\text{Sum of numbers}}{\text{Number of numbers}} \]

Using this formula, we can calculate the sum of the six numbers:

\[ \text{Sum of six numbers} = \text{Average} \times \text{Number of numbers} = 44 \times 6 = 264 \]

### Step 2: Calculate the sum of the two numbers.
The average of two of those numbers is given as 11. Again, using the average formula:

\[ \text{Sum of two numbers} = \text{Average} \times \text{Number of numbers} = 11 \times 2 = 22 \]

### Step 3: Calculate the sum of the remaining four numbers.
Now, we need to find the sum of the remaining four numbers. We can do this by subtracting the sum of the two numbers from the sum of the six numbers:

\[ \text{Sum of four numbers} = \text{Sum of six numbers} - \text{Sum of two numbers} = 264 - 22 = 242 \]

### Step 4: Calculate the average of the four numbers.
Now, we can find the average of the remaining four numbers using the sum we just calculated:

\[ \text{Average of four numbers} = \frac{\text{Sum of four numbers}}{\text{Number of numbers}} = \frac{242}{4} = 60.5 \]

### Step 5: Compare Quantity A and Quantity B.
- Quantity A (the average of the other four numbers) is 60.5.
- Quantity B is given as 77.

Now we can compare the two quantities:

\[ 60.5 < 77 \]

### Conclusion:
Since Quantity A (60.5) is less than Quantity B (77), the answer is that Quantity B is greater.

### Final Answer:
**Option 2: Quantity B is greater.**

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