Educerie · SAT · Math
Problem-Solving and Data Analysis · PSDA.2 Percentages
What you must be able to do
| You must be able to | What it looks like on the test |
|---|---|
| Increase and decrease by a percentage | …after a 15% discount |
| Find a percent change | …by what percentage did it increase? |
| Apply two changes in a row | The one that catches almost everybody |
| Work backwards to the original | …is 84, which is 70% of the original |
| Read "percent of" versus "percent more than" | A different calculation each time |
1The idea in one paragraph
Do percentages with multipliers, not with additions. An increase of 15% is × 1.15 and a decrease of 15% is × 0.85, and once everything is a multiplier the hard cases become easy: two changes in a row multiply, and working backwards means dividing. The single most valuable habit in this unit is never calculating "the percentage" as a separate number and then adding it on.
Two successive percentage changes never add. +20% then −20% is × 1.2 × 0.8 = × 0.96, a 4% loss.
2Multipliers
| English | Multiplier |
|---|---|
| 30% of | × 0.30 |
| increase by 30% | × 1.30 |
| decrease by 30% | × 0.70 |
| 30% more than | × 1.30 |
| 30% less than | × 0.70 |
3Successive changes
That gap between 23.5 and 25 is the whole question, and 25 is always one of the options.
4Percent change
(new − old) / old × 100. The denominator is always the original.
Rising and falling between the same two numbers are different percentages, because the base changes. The test asks this deliberately.
5Working backwards
After a 12% increase a price is 504 lira. What was it before?
Subtracting 12% of 504 gives 443.52, which is wrong and is offered as an answer. Whenever the question gives you the result and asks for the start, you divide.
6Percent of a total, and percentage points
A table gives counts and asks for a percentage: divide the part by the relevant total and be careful which total is meant — the row, the column, or everything.
And one piece of vocabulary: a rise from 20% to 25% is a rise of five percentage points, but a 25% increase. The test uses both phrases and they are not the same thing.
Where points are lost
- Adding successive percentages.
- Using the new value as the base for a percent change.
- Subtracting instead of dividing when working backwards.
- Confusing "30% of" with "30% more than".
- Taking the wrong total from a two-way table.
- Mixing percentage points with percent change.
Work it right
- Turn every percentage into a multiplier before calculating anything.
- For a chain of changes, multiply the multipliers.
- For a percent change, put the original underneath.
- To get back to an original, divide.
- Sanity-check: a discount must give a smaller number.
Try it
Q1. A coat priced at 380 lira is reduced by 25%. What is the sale price, in lira? (Type your answer.)
Q2. A town's population rose from 12,500 to 14,000. What was the percentage increase?
A) 10.7% B) 12% C) 15% D) 88.6%
Q3. A price is increased by 20% and then reduced by 20%. The final price is what percentage of the original?
A) 96% B) 98% C) 100% D) 104%
Q4. After a 35% discount, a chair costs 286 lira. What was the price before the discount, in lira?
A) 386.10 B) 420 C) 440 D) 817
Q5. In a survey, 45% of 800 respondents said they cycle to work. Of those, 20% also walk on some days. How many respondents both cycle and sometimes walk? (Type your answer.)
In one breath
Turn every percentage into a multiplier and the whole topic becomes multiplication: up 15% is × 1.15, down 15% is × 0.85, and two changes in a row multiply rather than add — which is why +20% then −20% leaves you at 96%, not back where you started. Percent change always divides by the original, and when the question hands you the result and wants the starting value, you divide rather than subtract.
Answers
Q1. 285. multiply by 0.75 380 × 0.75 = 285. Answering 95 gives the discount rather than the price.
Q2. B — 12%. divide the rise by the original
A divides by the new value. C and D use bases the question never sets.
Q3. A — 96%. 1.2 × 0.8 = 0.96 The second reduction is taken from a larger number than the first increase was taken from. C is the answer for a student who adds and subtracts the same percentage.
Q4. C — 440. the result is given, so divide
A adds 35% to 286, which uses the wrong base. B and D divide by the wrong multiplier.
Q5. 72. two multiplications, in order
Answering 160 applies both percentages to the 800 separately.
Educerie · written from the published College Board* Assessment Framework for the Digital SAT Suite *(Math, Problem-Solving and Data Analysis, skill/knowledge testing point "Percentages"). All questions and explanations are original Educerie text. Last reviewed 12 September 2026.
Check your understanding
The main ideas of this note. Tick each one you could do now, in an exam, without looking back up. Anything you cannot tick yet is the part to read again.