Question

A is 2 times B and B is 2 times C. The average of the reciprocals of A, B and C is 7/12. What is the value of A?

• A. 2
• B. 4
• C. 1
• D. None of these

Hint:

When solving problems involving averages, be careful to account for the relationships between variables and simplify them before substituting into equations.

Answer 1

The Correct Option is B

We know that:
\[ A = 2B \quad \text{and} \quad B = 2C \] So, \( A = 2B = 2 \times 2C = 4C \). The average of the reciprocals of A, B, and C is: \[ \frac{1}{A} + \frac{1}{B} + \frac{1}{C} = \frac{7}{12} \] Substitute \( A = 4C \) and \( B = 2C \) into the equation: \[ \frac{1}{4C} + \frac{1}{2C} + \frac{1}{C} = \frac{7}{12} \] Taking the LCM: \[ \frac{1}{4C} + \frac{1}{2C} + \frac{1}{C} = \frac{1 + 2 + 4}{4C} = \frac{7}{4C} \] Now, equating this to \( \frac{7}{12} \): \[ \frac{7}{4C} = \frac{7}{12} \] Cross-multiply: \[ 4C = 12 \] So, \( C = 3 \), and hence \( A = 4C = 4 \times 3 = 12 \).
Thus, the correct answer is \( A = 4 \).