Percent questions are everywhere on the GMAT Focus: discounts and markups in Quant, growth and share figures in Data Insights tables and graphs, and interest problems in both. The mathematics is simple. The errors come from picking the wrong base.
Turn every percent change into a multiplier. A 20% increase is × 1.2, a 15% decrease is × 0.85, and successive changes multiply: up 20% then down 20% is 1.2 × 0.8 = 0.96, a 4% net loss. Percent change always uses the starting value as the base, so going from 80 to 100 is a 25% increase, while going from 100 back to 80 is a 20% decrease.
Reverse questions ask for the original value. If a price after a 25% markup is \$150, divide by 1.25 to get \$120; subtracting 25% of \$150 is the classic wrong answer. For simple interest, interest = principal × rate × time; for compound interest, multiply by (1 + r) once per period.
Picking 100 as a starting value turns most percent questions into arithmetic you can do in your head. In Data Sufficiency, remember that percentages alone never give an absolute amount: knowing a price rose 10% says nothing about the price itself.
4 practice questions
Data SufficiencyPercents and Interest ProblemsEasy
Question 1
A jacket originally priced at 80 dollars was put on sale at a discount. What was the sale price of the jacket?
(1) The discount was 15% of the original price.
(2) The discount reduced the price by 12 dollars.
AStatement (1) ALONE is sufficient, but statement (2) ALONE is NOT sufficient.
BStatement (2) ALONE is sufficient, but statement (1) ALONE is NOT sufficient.
CBOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
DEACH statement ALONE is sufficient.
EStatements (1) and (2) TOGETHER are NOT sufficient.
Show answer & explanation
Correct answer: D
Key Concept or Approach
Sale price = original price − discount. With the original price known, either the discount rate or the discount amount determines the sale price.
Common trap: A: students overlook that a dollar discount works just as well as a percent discount when the original price is known.
Data SufficiencyPercents and Interest ProblemsEasy
Question 2
A bookstore's total revenue in 2025 was greater than its total revenue in 2024. By what percent did the revenue increase from 2024 to 2025?
(1) The bookstore's revenue in 2025 was $48{,}000$ dollars more than its revenue in 2024.
(2) The bookstore's revenue in 2024 was $80\%$ of its revenue in 2025.
AStatement (1) ALONE is sufficient, but statement (2) ALONE is NOT sufficient.
BStatement (2) ALONE is sufficient, but statement (1) ALONE is NOT sufficient.
CBOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
DEACH statement ALONE is sufficient.
EStatements (1) and (2) TOGETHER are NOT sufficient.
Show answer & explanation
Correct answer: B
Key Concept or Approach
Percent increase $= \frac{R_{25} - R_{24}}{R_{24}} \times 100\%$, which depends only on the ratio $\frac{R_{25}}{R_{24}}$. A dollar difference alone does not fix a ratio.
Step-by-Step Solution
Step 1: Statement (1): $R_{25} - R_{24} = 48{,}000$. If $R_{24} = 48{,}000$ the increase is $100\%$; if $R_{24} = 192{,}000$ the increase is $25\%$. Not sufficient.
Step 2: Statement (2): $R_{24} = 0.8R_{25}$, so $\frac{R_{25}}{R_{24}} = \frac{1}{0.8} = 1.25$, an increase of $25\%$. Sufficient.
Step 3: Only statement (2) answers the question.
Final Answer
Answer: B
Common trap: A: the concrete 48,000 figure looks decisive, and some read (2) as a 20% change (80% of 2025 means 2025 is 25%, not 20%, above 2024).
Data SufficiencyMixture ProblemsPercents and Interest ProblemsMedium-hard
Question 3
Solution P is $20\%$ salt by volume and solution Q is $50\%$ salt by volume. Some of P and some of Q are combined to form mixture M. What percent of M, by volume, is salt?
(1) M contains $6$ more liters of Q than of P.
(2) M has a total volume of $36$ liters.
AStatement (1) ALONE is sufficient, but statement (2) ALONE is NOT sufficient.
BStatement (2) ALONE is sufficient, but statement (1) ALONE is NOT sufficient.
CBOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
DEACH statement ALONE is sufficient.
EStatements (1) and (2) TOGETHER are NOT sufficient.
Show answer & explanation
Correct answer: C
Key Concept or Approach
With $p$ liters of P and $q$ liters of Q, the salt percent of M is $\frac{0.2p + 0.5q}{p + q}$, which depends only on the ratio of P to Q.
Common trap: A: students treat '6 more liters of Q' as fixing the proportion, but a fixed difference gives a different ratio at every total volume.
Problem SolvingPercents and Interest ProblemsHard
Question 4
A sum of money invested for $2$ years at an annual rate of $r$ percent earns $\$1{,}200$ in simple interest. The same sum invested for $2$ years at $r$ percent compounded annually would earn $\$1{,}272$ in interest. What is the value of $r$?
A$6$
B$8$
C$10$
D$11$
E$12$
Show answer & explanation
Correct answer: E
Key Concept or Approach
Over 2 years, compound minus simple interest is the interest earned on the first year's interest.
Step-by-Step Solution
Step 1: Simple: $2P\frac{r}{100} = 1200$, so one year's interest is $P\frac{r}{100} = 600$.
Step 2: The extra $\$72$ is interest on that $\$600$ for one year: $600 \cdot \frac{r}{100} = 72$.
Step 3: $r = 12$ (principal $\$5{,}000$).
Final Answer
Answer: E
Common trap: 6 - dividing 72 by the full 1,200 instead of by one year's interest of 600.
