SAT Percentages
Percent of, percent change, reverse percent, percent-of-percent.
How to score it
- Percent change = (new − old) / old — the base is always the original.
- “Percent of a percent” → multiply the decimals, never add.
- Reverse percent: the final is (1 ± p) times the original; divide to undo.
Common traps
- Uses the new value as the base for percent change.
- Adds two percentages instead of multiplying.
- Treats a reverse-percent problem as a forward one.
The 4 question types, with real examples
Percent change / K is what % of M
“What was the percent [increase / decrease] from a to b?”
18 is what percent of 72?
- A4%
- B25%✓
- C54%
- D400%
The percentage is (18/72) × 100 = 0.25 × 100 = 25%.
Reverse percentage (find the original)
“[Final] is p% [more / less] than the original. What is the original?”
After a 15% discount, the price of a television is $340. What was the original price, in dollars?
- A✓
- B
- C
- D
The discounted price is 85% of the original price. If x is the original price, then . Solving gives .
Percent of a percent
“What percent of the whole group is [both attributes]?”
In a library, 35% of the books are fiction. Of all the fiction books, 40% are mysteries. What percentage of all the books in the library are fiction mysteries?
- A75%
- B12%
- C14%✓
- D5%
The fiction mysteries are 40% of the fiction books, which are 35% of all books. Therefore, fiction mysteries are 0.40 × 0.35 = 0.14 or 14% of all books.
What is N% of M (literal)
“What is [n]% of [m]?”
A store's revenue in January was $48000. If the revenue in February was 25% greater than the revenue in January, what was the revenue, in dollars, in February?
- A$12000
- B$36000
- C$60000✓
- D$73000
The revenue in January was $48000. A 25% increase means the revenue in February was 48000 + 0.25(48000) = 48000 + 12000 = 60000 dollars.
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