How to Ace the Percentage Questions in the GRE?

Percentage questions in GRE exam can appear to be a bit difficult to ace. However, with the right strategies and grasp on basics, a student can easily score well in these tricky questions.

Percentages are an important part of GRE quant section as they can be used in questions ranging from simple to complex ones. Questions can be based entirely on percentages or can be combined with other quant topics as well. Therefore, having a strong understanding of percentages can help a student in boosting their score and problem-solving abilities.

If you are looking to get a strong hold on GRE percentage questions, then you are at the right place. Keep reading further to know more!

Understanding Percentages

Percentages are a way of expressing a number as a fraction of 100. They are often used to compare proportions and describe how one quantity relates to another. The basic formula for calculating a percentage is:

Percentage = (part/whole) x 100

Different Percentage Question Types/Formulas

There are different types of percentage questions asked in the GRE exam. Below we have discussed various types of percentage questions asked in the GRE which will help you gain mental clarity:

• Finding a Percentage of a Number

To find a percentage of a number, multiply it by the percentage (converted into a decimal).

Example: What is 20% of 150?

1. Convert 20% to a decimal: 20% = 0.20
2. Multiply 0.20 by 150: 0.20 × 150 = 30

• Finding What Percentage One Number Is of Another

To find what percentage one number is of another, divide the part by the whole and then multiply by 100.

Example: What percentage is 30 of 150?

1. Divide 30 by 150: 30/150 = 0.20
2. Convert 0.20 to a percentage: 0.20 x 100 = 20%

• Increasing or Decreasing a Number by a Percentage

To increase the number by a percentage, calculate the percentage of the number and then add it to the original number. To decrease it, subtract the calculated percentage from the original number.

Example (Increase): Increase 200 by 15%.

1. Find 15% of 200: 0.15 x 200 = 30
2. Add it to 200: 200 + 30 = 230

Example (Decrease): Decrease 200 by 15%.

1. Find 15% of 200: 0.15 × 200=300
2. Subtract it from 200: 200 − 30=170

• Percentage Change

To find the percentage change between an old value and a new value, use the formula:

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

Example: If a stock price increases from $50 to $60, what is the percentage increase?

1. Calculate the change: 60 − 50 = 10
2. Divide by the old value = 10/50 = 0.20
3. Convert to percentage = 0.20 x 100 = 20%

• Compound Percentage Problems

These problems involve multiple percentage changes applied one after the other. To solve these, apply each percentage change sequentially.

Example: A salary increases by 10% and then by another 20%. If the original salary is $1,000, what is the final salary?

1. First increase: 1000 × 1.10 = 1100
2. Second increase: 1100 x 1.20 = 1320

There is also a direct formula to calculate the net percentage change in case of two successive percentage changes. Mentioned below are three cases of two successive percentage change and their respective direct formula to calculate net percentage change:

1. Both percentage changes are negative: x and y both are negative and imply a clear decrease= (-x-y+xy/100)%

1. Both percentage changes are positive: x and y are positive and net increase = (x+y+xy/100) %.

1. One percentage change is positive and the other is negative: x is positive and y is negative, then net percentage change = (x-y-xy/100)%

Sample GRE Percentage Questions and Answer Explanations

Let us now go through some GRE sample questions and answer explanations which will help you understand better.

Q1. If there were 800 employees working in a cycle factory and 25% of employees were absent on a certain day, then how many employees were absent on that day?

Ans. Note: Essentially, we want to find out — what 25% of 800 is.
Let’s translate!
‘%’ means ‘over 100’, and ‘of’ means ‘multiplication’.
Thus, 25% of 800 means the answer is 200.

Q2. John’s video game collection contains 600 games. Samantha’s video game collection contains 500 games. Is Samantha’s video game collection what percent smaller than John’s? Ignore the percent sign and round off your answer to the nearest tenth place.

Ans. Note: It’s important to note down the phrase ‘Percent smaller’ in this question, as this will help us decide the value for the original number. ‘Percent smaller’ indicates that the original number should be the bigger number out of the two. In this case, it is 600. Since the difference between the two numbers is 100, we get
Percentage decrease=100/600 × 100 = 50/3 = 16.7

Q3. A radio that sells for $200 is on sale for $160. Sherlock purchased the radio at the normal price, and Michael purchased the radio during the sale. By what percent was the price Sherlock paid more than the price paid by Michael?

Ans. Note: This is a percent question asking for ‘percent more, so recall the formula
Percentage change= Difference/original x 100.

Here, the difference is clearly $40. Now, picking up the right number for the original is the challenge. Most of us may be quick to pick $200. But take a moment and recall that we learned that if the question is asking for “what percent more”, then the original number is the smaller number out of the two.

Assuming the original number is always the first number in the question is folly. Don’t fall into the trap. Let the phrases “percent increase/more/greater” and “percent decrease/less/smaller” help you decide what the original number is.

So, the right value for the original number in the above question is $160. Therefore,

Percentage increase = 40/160 × 100 = 25

Hence, the answer is 25%. Fill only 25 in the numeric entry box. Typing 0.25 will be incorrect and will not yield any credit.