Percent Increase and Decrease
A percent change is always measured against the original amount. Multiplying by a single factor is usually faster than adding and subtracting.
Reading the concept isn't enough. The score comes from practicing the real Bluebook-style format and finding the exact mistakes you keep making.
What the SAT tests here
To increase by $r\%$, multiply by $1 + \frac{r}{100}$; to decrease, multiply by $1 - \frac{r}{100}$. The base is the starting value, not the new one.
How to solve one, step by step
Example: increase $\$80$ by $25\%$.
- Multiply by $1.25$: $80 \times 1.25$.
- Result: $\$100$.
The mistakes that cost points
- Using the new value as the base. Percent change is relative to the original amount.
- Subtracting the percent wrong in a decrease. A $25\%$ decrease multiplies by $0.75$, not $0.25$.
Practice questions
Try these the way you would on test day, then open the solution to check your method.
Easy
A jacket is discounted from $\$80$ to $\$k$ after a $25\%$ decrease. What is the value of $k$?
- A$k = 60$
- B$k = 25$
- C$k = 55$
- D$k = 100$
Show solution
Answer: A, $k = 60$. Decrease $= 25\%$ of $\$80 = 0.25 \times 80 = 20$. New price $= 80 - 20 = \$60$.
Medium
A store raises a price by $k\%$. The original price is $\$50$ and the new price is $\$63$. What is the value of $k$?
- A$k = 74$
- B$k = 26$
- C$k = 20.6$
- D$k = 13$
Show solution
Answer: B, $k = 26$. $k = \frac{63 - 50}{50} \times 100 = \frac{13}{50} \times 100 = 26\%$.
Hard
A store marks down a price by $k\%$. The new price is $\$51$ and the original price was $\$60$. What is the value of $k$?
- A$k = 15$
- B$k = 17.6$
- C$k = 9$
- D$k = 85$
Show solution
Answer: A, $k = 15$. $k = \frac{60 - 51}{60} \times 100 = \frac{9}{60} \times 100 = 15\%$.
Find your exact gaps
Take a free, full-length practice test and see precisely which question types trip you up.
Practice this for freeNo credit card. Register once, take as many tests as you like.