GRE Percent Questions Practice Questions with Answers

Calculating a percentage involves expressing a number as a fraction of 100, which serves as a fundamental skill for the Quantitative Reasoning section. Whether you are analyzing data in a chart or solving a complex word problem, GRE percent questions require a firm grasp of ratios, decimal conversions, and algebraic manipulation. According to the Educational Testing Service (ETS), these concepts appear frequently across both Discrete Question and Data Interpretation formats. To succeed on the exam, you must be comfortable moving between parts, wholes, and rates under timed conditions. Using tools like a personalized study plan can help you allocate enough time to master these nuances before test day.

Concept Explanation

GRE percent questions assess your ability to interpret and calculate values relative to a base of 100. At its core, the word percent means "per centum" or "out of one hundred." Most problems on the GRE revolve around three primary components: the part, the whole (or base), and the percentage rate. These are traditionally related by the formula:

$$\text{Part} = \frac{ \text{Percent}}{100} \times \text{Whole}$$

Beyond basic calculations, the GRE frequently tests percent change. This measures the increase or decrease of a value relative to its original starting point. The formula for percent change is:

$$\text{Percent Change} = \frac{ \text{New Value} - \text{Old Value}}{ \text{Old Value}} \times 100$$

Another common trap involves successive percent changes. If a price increases by 20% and then decreases by 20%, the final price is not the original price. This is because the second change is calculated based on the new, intermediate value, not the initial one. Understanding this relationship is a core part of GRE Prep and is vital for avoiding common pitfalls. You should also be familiar with translating English phrases into math: "is" means equals (=), "of" means multiply ($\times$), and "what" represents the variable ($x$).

Solved Examples

1. Basic Percent Calculation: What is 15% of 80?
   1. Identify the whole (80) and the percentage (15%).
   2. Set up the equation: $x = \frac{15}{100} \times 80$.
   3. Simplify the fraction: $x = 0.15 \times 80$.
   4. Calculate the final result: $x = 12$.
2. Percent Increase: A jacket originally priced at $120 is on sale for $150. What is the percent increase in price?
   1. Identify the old value ($120) and the new value ($150).
   2. Calculate the difference: $150 - 120 = 30$.
   3. Divide the difference by the original value: $\frac{30}{120} = \frac{1}{4}$.
   4. Convert the fraction to a percentage: $0.25 \times 100 = 25\%$.
3. Successive Changes: A stock's value increases by 10% on Monday and then decreases by 10% on Tuesday. If the starting value was $100, what is the final value?
   1. Calculate the value after Monday: $100 + (0.10 \times 100) = 110$.
   2. Calculate the decrease based on the new value ($110): $110 - (0.10 \times 110)$.
   3. Subtract the decrease: $110 - 11 = 99$.
   4. The final value is $99.

Practice Questions

1. If 25% of a number is 40, what is 15% of that same number?

2. A laptop is discounted by 20%, and then an additional 10% is taken off the discounted price. What is the total percentage discount from the original price?

3. In a class of 40 students, 60% are female. If 5 more female students join the class, what percentage of the class will be female?

4. If $x$ is 200% of $y$, then $y$ is what percent of $x$?

5. The price of a gallon of gas increased from $3.00 to $3.75. What was the percent increase?

6. A merchant buys an item for $80 and sells it for a price that is 25% greater than the cost. If a customer uses a coupon for 10% off the selling price, how much does the customer pay?

7. If the radius of a circle increases by 50%, by what percent does the area of the circle increase?

8. Quantity A: 45% of 80 | Quantity B: 80% of 45. Compare the two quantities.

9. A jar contains red, blue, and green marbles. 30% are red, and 40% are blue. If there are 12 green marbles, how many total marbles are in the jar?

10. A worker's salary was increased by 15% to $46,000. What was the original salary?

Answers & Explanations

1. Answer: 24. First, find the number: $0.25x = 40 \rightarrow x = 160$. Then find 15% of 160: $0.15 \times 160 = 24$.
2. Answer: 28%. Assume the original price is $100. After the 20% discount, the price is $80. A 10% discount on $80 is $8. The final price is $80 - 8 = 72$. The total discount is $100 - 72 = 28$.
3. Answer: 64.44% (approx). Initially, there are $0.60 \times 40 = 24$ females. Adding 5 makes 29 females. The new total students is $40 + 5 = 45$. $\frac{29}{45} \times 100 \approx 64.44\%$.
4. Answer: 50%. If $x = 2y$, then $y = \frac{1}{2}x$. One half is equal to 50%.
5. Answer: 25%. Difference is $3.75 - 3.00 = 0.75$. Percent increase is $\frac{0.75}{3.00} = \frac{1}{4} = 25\%$.
6. Answer: $90. Selling price is $80 \times 1.25 = 100$. Customer pays 10% less than 100: $100 - 10 = 90$.
7. Answer: 125%. Area is $\pi r^2$. New radius is $1.5r$. New area is $\pi (1.5r)^2 = 2.25 \pi r^2$. The increase is $2.25 - 1.00 = 1.25$, or 125%.
8. Answer: They are equal. $0.45 \times 80 = 36$ and $0.80 \times 45 = 36$. In percent problems, $a\% \text{ of } b$ always equals $b\% \text{ of } a$.
9. Answer: 40. Red and blue make up 70% (30 + 40). Thus, green marbles represent 30% of the total. $0.30 \times \text{Total} = 12$. $\text{Total} = \frac{12}{0.30} = 40$.
10. Answer: $40,000. Let $S$ be the original salary. $1.15S = 46,000$. $S = \frac{46,000}{1.15} = 40,000$.

1. If a value increases from 200 to 250, what is the percentage increase?

• A20%
• B25%
• C50%
• D15%

Frequently Asked Questions

How do I handle percent change on the GRE?

Always identify the "original" value first, as this serves as your denominator. Subtract the old value from the new value and divide that difference by the original value to find the decimal change.

Can a percentage be greater than 100?

Yes, percentages greater than 100 indicate that the part is larger than the original whole. For example, 250% of 10 is 25, which is common in growth or inflation problems.

What is the fastest way to calculate 15% without a calculator?

Find 10% by moving the decimal one spot to the left, then find 5% by halving that 10% value. Add the two results together to get the total 15%.

Why does a 20% increase followed by a 20% decrease not return to the original number?

The second percentage change is applied to a different base value than the first. Because the base for the decrease is larger than the original base, the absolute value of the decrease is larger than the initial increase.

Does the GRE provide a calculator for percent questions?

The GRE provides an on-screen calculator for the Quantitative Reasoning section. While helpful for long division, understanding the underlying logic of proportions (similar to scientific data analysis) is faster for simple percentages.