This domain is all about ratios, rates, percentages, proportions, and statistics — the "real-world math" questions. They're wordy, so careful reading beats clever tricks.
Percent translation: "of" → multiply, "is" → equals, "what" → the variable. "15 is 20% of what?" becomes 15 = 0.20 × n.
The essentials
- Percent change = (new − old) / old × 100. Always divide by the original.
- Discount: a 25% discount means you pay 75%. Final = 0.75 × original.
- Rate = quantity ÷ time. Set up a proportion for "at that rate" questions.
- Mean = sum ÷ count → so sum = mean × count. This rearrangement unlocks most average questions.
- Median = middle value when ordered; resistant to outliers, unlike the mean.
Two-step percent trap: A price up 20% then down 20% is NOT back to start — it's 0.80 × 1.20 = 0.96, a 4% net drop. Percentages don't cancel.
Worked examples
A jacket costs $80 after a 20% discount. What was the original price?
- A 20% discount means you pay 100% − 20% = 80% of the original price.
- So $80 is 80% of the original: 80 = 0.80 × p.
- Divide: p = 80 ÷ 0.80 = $100.
- Check: 20% of $100 is $20, and $100 − $20 = $80 ✓. (Note: it is NOT $80 + 20% = $96 — that's the classic trap.)
The average of 6 numbers is 15. If one number, 25, is removed, what is the new average?
- Use sum = mean × count: the total of all 6 numbers is 15 × 6 = 90.
- Remove 25: the new sum is 90 − 25 = 65.
- There are now 5 numbers, so the new average is 65 ÷ 5 = 13.
A price rises 20%, then falls 20%. What is the net change?
- Start with $100 to make it concrete.
- Up 20%: 100 × 1.20 = $120.
- Down 20% from $120: 120 × 0.80 = $96.
- Net change: $96 vs $100 — a 4% DECREASE. Percent increases and decreases do not cancel out.
Common mistakes to avoid
- Dividing by the new value instead of the original when computing percent change. Always divide by the ORIGINAL.
- Assuming a 20% increase followed by a 20% decrease returns to the starting value. It does not — you end up 4% lower.
- Confusing 'percent of' with 'percent more than.' 'B is 20% of A' and 'B is 20% more than A' are completely different.
- Forgetting to put numbers in order before finding the median.