GRE Percentage Questions: Types, Formulas, Sample Problems

Percentage questions on the GRE can be quite tricky to deal with. Students require adequate practice and effective strategies to solve these percentage-based problems. Percentage questions from the GRE Arithmetic section can range from simple to complex where some questions can also be combined with other quant topics. One should have a thorough understanding of percentages and how they work in order to solve these problems effectively.

If you’re looking to ace the GRE percentage Questions, this post provides you with all the information you need to do so!

Percentage Basics: What you need to know?

Percent represents a value as a fraction of one hundred, used to express proportions and compare quantities. It is denoted by the symbol %. The formula for calculating percentage is as follows,

Percentage = (part/whole) x 100 

Let’s take a basic real life example to understand percentage. 

Example: A student scores 35 out of 50 on their exam. How do we calculate the percentage of their score?

We apply the formula mentioned above,
Part = 35
Whole = 50

Percentage: (35/50) x 100 = 70%

The student has scored 70% on their exam.

Types of Percentage Questions in the GRE

Percentage questions are an important part of the GRE Quant section. Let’s take a look at the various types of percentage questions that can appear in the GRE. Getting yourself familiar with the below mentioned question types will help you ace the GRE percent problems.

Convert Percentages to Decimals

To convert a percentage to a decimal, drop the percent sign and move the decimal points two places to the left. If necessary, add zeros to the left of the percent to allow for the correct location of the decimal point.

Example: Convert 14% to a decimal.

14% = 0.14

Convert Decimals to Percentages

To convert a decimal to a percent, move the decimal point to the right and then add percent sign. If necessary, add zeros to the right of the percent to allow for the correct location of the decimal point.

Example: Convert the decimal 0.28 to percent.

0.28 = 28%

Convert Percentages to Fractions

To convert a percent to a fraction, first convert the percent to a decimal and then convert the decimal to a fraction.

Example: Convert 75% to a fraction.

1. Convert 75% to a decimal: 75% = 0.75
2. Convert 0.75 to a fraction: 0.75 = 75/100 = 3/4

Convert Fractions to Percentages

To convert a fraction to percentage, first convert the fraction to a decimal, then convert the decimal to a percent.

Example: Convert 1/4 to a percent.

1. Convert 1/4 to a decimal: 1/4 = 0.25
2. Convert 0.25 to a percent: 0.25 = 25%

Find the percentage of a Number

To find the percentage of a number: Convert the percent into a decimal first. Then, multiply the decimal number with the actual number. 

Example: What is 40% of 200?

1. Convert 40% to a decimal: 40% = 0.40
2. Multiply 0.40 by 200: 0.40 x 200 = 80

Find what percentage one number is of another

To find what percentage one number is of another: Divide the part number by the whole number and then multiply the result by 100.

Example: What percentage is 60 of 200?

1. Divide 60 by 200: 60/200 = 0.30  
2. Convert 0.30 to a percentage: 0.30 x 100 = 30%

Increase or decrease one number by a percentage

Increase: To increase a number by a certain percentage, find the percentage of the respective number and then add the result to the original number.

Example: Increase 300 by 20%

1. Find 20% of 300: 0.20 x 300 = 60
2. Add it to 300: 300 + 60 = 360

Decrease:  To decrease a number by a certain percentage, find the percentage of the respective number and then subtract the result from the original number.

Example: Decrease 300 by 20%

1. Find 20% of 300: 0.20 x 300 = 60
2. Subtract it from 300: 300 - 60 = 240

Percentage change problems

To find the change in percentage between an old value and a new value, apply the formula given below,

Percentage Change = (New Value - Old Value / Old Value) x 100

Example: If the price of a product increases from Rs.40/- to Rs.50/-, how much is the percentage change?

1. Calculate the difference: 50 - 40 = 10
2. Divide the result by the old value: 10/40 = 0.25
3. Convert to percentage = 0.25 x 100 = 25%

The percentage change in the product price is 25%.

Compound percentage problems

In compound percentage problems, there are multiple percentage changes involved. These problems must be solved by applying the percentage changes one after the other.

Example: The bus fare is increased by 10% followed by another 20%. If the original bus fare is  Rs.10/-, what is the final bus fare?

1. First Increase: 10 x 1.10 = 11
2. Second Increase: 11 x 1.20 = 13.2

The final bus fare after two consecutive hikes is Rs. 13.2/-

Sample GRE Percentage Questions and Answers

Refer to the below given GRE percentage sample questions and answers to help you practice.

1. A store owner paid Rs.60/- for a hat and plans to mark up the price by 12%. What would be the selling price for the hat?

Solution: Find 12% of 60: 60 x 0.12 = 7.2
Add the result to the original value = 60 + 7.2 = 67.2

The selling price for the hat is Rs. 67.2/-.

2. A lamp was usually sold for Rs.80. It was discounted 20%. What was the sale price of the lamp?

Solution: Find 20% of 80: 80 x 0.20 = 16
Deduct the result from 80: 80 - 16 = 64

The sale price of the lamp is Rs. 64/-. 

3. A vase was purchased at a wholesale warehouse for Rs.120/-. The vase was marked up 40% in a retail store. The store owner sold the vase at a 25% discount sale. What was the selling price of the vase?

Solution: Cost of the vase = 120
Retail price: 
Find 40% of 120: 120 x 0.4 = 48 
Now add the result with 120: 120 + 48 = 168.
The retail price of the vase is Rs.168/-.

Sale price:
Find 25% of 168: 168 x 0.25 = 42
Now add the result with 168: 168 + 42 = 210.
The selling price of the vase is Rs.210/-.

4. In a restaurant, a meal costs Rs.32.75. There is a 6% tax to be added on before you get the bill. If you leave the wait staff a 20% tip, what was the total cost of a meal?

Solution: Cost of meal = Rs.32.75

Meal with tax: 
Find 6% of 32.75: 32.75 x 0.06 = 1.965
Add the result with cost = 1.965 + 32.75 =  34.72

Meal with tax and tip:
Find 20% tip amount: 34.72 x 0.2 = 6.944
Add the result with cost: 6.944 + 34.72 = 41.66

The total cost of the meal is = Rs.41.66/-

5. A shirt sold for Rs.150 at a 25% off sale. What was the original price of the shirt?

Solution: 

100% - 25% = 75%
The sale price is 75% of the original price.

150/0.75 = 200

The sales price of the shirt is Rs.200/-

Tips to ace the percentage questions in the GRE

Here are some valuable tips to help you ace the percentage questions in the GRE,

• Master Percentage Basics: Gain a complete understanding of the basics of Percentages and ensure you are familiar with all the core concepts. Master all common question types like converting between fractions, decimals and percentages, along with percentage changes and other percentage world problems.
• Practice Mental Math for Quick Calculations: Practice calculating common percentages mentally to speed up the process and save time during the exam. This skill will come in handy for approximation-based calculations, allowing you to estimate the answers quickly. 
• Formulate Equations Carefully: Most of the percentage questions require setting  equations. Identify the variables and the right formula to be used for that particular question. 
• Identify and avoid common errors: As the GRE percentage questions often involve tricky wording, pay close attention to terms like “percent of”, “more than”, or “less than” to avoid misinterpretation.
• Practice Real GRE Questions: Practice more GRE-style percentage questions to get yourself familiar with the pattern. The more you practice the more confidently you can take on the questions during the exam. 

Percentage Questions are an integral part of the GRE Quant section. This post serves as a comprehensive guide by covering various percentage calculations, formulas, question types, and sample questions with answers. For personalised GRE coaching sessions, reach out to our expert faculty by filling the enquiry form.