Question

The arithmetic mean of \( a, b, c, d \) is 14.
Quantity A: 32
Quantity B: The arithmetic mean of \( a + b \), \( c + d \), and \( a - b + c - d = 48 \)

• A. Quantity A and Quantity B are equal.
• B. Quantity A is greater.
• C. Quantity B is greater.
• D. The relationship between Quantity A and Quantity B cannot be determined.

Hint:

When given the arithmetic mean, use the sum of the numbers and divide by the number of terms to find the mean.

Answer 1

The Correct Option is C

Step 1: Given the arithmetic mean of \( a, b, c, d \). The arithmetic mean of \( a, b, c, d \) is given by: \[ \frac{a + b + c + d}{4} = 14 \Rightarrow a + b + c + d = 56. \]
Step 2: Work with the second condition. We are asked for the arithmetic mean of the quantities \( a + b \), \( c + d \), and \( a - b + c - d \). We have: \[ a + b + c + d = 56 \quad \text{and} \quad a - b + c - d = 48. \] Thus, the arithmetic mean is: \[ \frac{56 + 48}{3} = 34.67. \]
Step 3: Conclusion. So, Quantity B is greater than Quantity A.