GRE General TestQuantitative ReasoningMedium
A quality control engineer inspects a batch of 500 components. He finds that 4% of the components are defective. If he then re-inspects the defective components and finds that 25% of them were actually acceptable, how many components are truly defective?
- A25
- B15
- C20
- D30
Show answer & explanationAnswer & explanation
Correct answer: B. 15
Total components = 500. Initially defective components = 4% of 500 = 0.04 * 500 = 20. Of these 20, 25% were acceptable, meaning 75% were truly defective. Truly defective = 20 * (1 - 0.25) = 20 * 0.75 = 15.
Why the other options are wrong
- A. This is 5% of the total components (500 * 0.05), which is incorrect.
- C. This is the initial number of components identified as defective, not the truly defective count.
- D. This is 6% of the total components (500 * 0.06), which is incorrect.
Multi-Step Percentage Problems
Problems requiring multiple percentage calculations applied sequentially, where each step's result becomes the base for the next calculation.
- Work through the problem step-by-step.
- Be careful to apply percentages to the correct base value at each stage.
- Often involves finding a percentage of a percentage.
Memory trick: Each percentage is a filter, apply them in order.