Mean proportional (geometric mean): Find the mean proportional between 9 and 64 (i.e., find x such that 9 : x = x : 64).
Aptitude
Ratio and Proportion
Difficulty: Easy
Choose an option
Answer
Correct Answer: 24
Explanation
Introduction / Context:The mean proportional (geometric mean) x between a and b satisfies a : x = x : b, or x^2 = a * b. This is a standard concept in ratio and proportion and geometric mean computations.
Given Data / Assumptions:
- a = 9.
- b = 64.
- Find x such that x^2 = a * b.
Concept / Approach:Compute the product a * b and then take the positive square root, since a and b are positive.
Step-by-Step Solution:x^2 = 9 * 64 = 576.x = sqrt(576) = 24.
Verification / Alternative check:Check proportionality: 9 : 24 = 3 : 8 and 24 : 64 = 3 : 8, confirming correctness.
Why Other Options Are Wrong:
- 25, 27, 35 are not the square root of 576 and do not keep equal ratios with 9 and 64.
Common Pitfalls:
- Confusing third proportional with mean proportional.
- Arithmetic mistakes in multiplying or in the square root.
Final Answer:24