Lessons · Quantitative Reasoning
CLT Quantitative Reasoning · Lesson
Percents
A percent is a fraction of 100. Percent change is (new − old) ÷ old. Successive changes multiply; they do not add.
- Turn "percent of" into multiplication: 15% of 80 is 0.15 × 80 = 12.
- For an increase of p%, multiply by (1 + p/100); for a decrease, by (1 − p/100).
- For "what was the original price," divide by the multiplier instead of subtracting the percent.
Q. A price rises 20%, then falls 20%. What is the overall change?
Answer A 4% decrease.
100 × 1.2 = 120, and 120 × 0.8 = 96. The second 20% is taken from a larger number.
- Thinking +20% then −20% returns to the start.
- Finding the original price by taking the percent off the new price. If $60 is after a 25% discount, the original is 60 ÷ 0.75 = $80, not $75.
Every practice question comes with a full explanation, including why each wrong choice is wrong. Free, with no account.