GED Mathematical Reasoning TestQuantitative Problem Solving with Rational NumbersMedium
A quality control inspector checks 120 items. She finds that 15% of the items have minor defects and 5% have major defects. What fraction of the inspected items have no defects?
- A4/5
- B7/10
- C1/5
- D3/4
Show answer & explanationAnswer & explanation
Correct answer: A. 4/5
First, find the total percentage of defective items: 15% (minor) + 5% (major) = 20%. Then, subtract this from 100% to find the percentage with no defects: 100% - 20% = 80%. Finally, convert 80% to a fraction: 80/100, which simplifies to 4/5.
Why the other options are wrong
- B. Incorrect. This is 70%, which implies 30% defective.
- C. Incorrect. This is 20% or 1/5, which is the fraction of defective items.
- D. Incorrect. This is 75%, which would mean 25% defective.
Percentage to Fraction Conversion
Converting a percentage to a fraction involves writing the percentage as a fraction with a denominator of 100 and then simplifying the fraction to its lowest terms.
- A percentage represents 'parts per hundred'.
- Write the percentage number as the numerator over 100.
- Simplify the fraction by dividing both numerator and denominator by their greatest common divisor.
- The total number of items (120) is extraneous information for finding the *fraction* with no defects.
Memory trick: Percent over a hundred, then simplify till it's done.