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3.2.9 Percent change
Achievable GRE
3. Quantitative reasoning
3.2. Arithmetic & algebra

Percent change

You can save a lot of time by learning the quickhand ways to solve for percentage changes. But before we get into a few tricks, let’s first make sure we understand percentage changes well. You probably intuitively know that 50% of 100 is 50, but how about:

What is 50% more than 100?

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Answer: 150

Since 50% of 100 is 50, then 50% more is 100 + 50 = 150.

Fully as math:

It’s important to know how to go the other way too:

What is 50% less than 100?

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Answer: 50

Since 50% of 100 is 50, then 50% less is 100 - 50 = 50.

Fully as math:

How about with numbers that are a bit harder?

What is 40% more than 990?

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Answer: 1386

And the other way:

What is 40% less than 990?

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Answer: 594

There’s a quicker way to solve these operations. Since percentages add up to 100%, 40% less of something is equivalent to 60% of something. Try it out with 990:

This matches the result we found earlier. This is because the 40% is subtracted from the original 100%, leaving us with 100% - 40% = 60% of the original.

Similarly, 40% more of something equals 100% + 40% = 140% of something.

Whether you use the 100% trick or not is up to you! What’s most important is that you can express the question in a proper math equation, since from there, solving it is straightforward.

Example percent change GRE question

Let’s try a GRE question using these techniques.

There are three variables: , , and . If both and are decreased by 10%, becomes 25% greater than , and 50% greater than the decreased value of . What percent of is the original value of ? Round to the nearest percent.

Try it yourself, and then check your work.

(spoiler)

Answer: 93%

First, let’s review some of the basics. Decreasing something by 10% is the same as multiplying it by . Increasing something by 25% is the same as multiplying it by , and increasing something by 50% is the same as multiplying it by . We can use these facts to create the following equations:

Since the left side of these two equations are the same (), we can set the right sides equal to each other. This will leave us with only the and variables, and we can simplify the math.

The question asks us:

What percent of is the original value of ?

We have expressed in terms of , but we have it in terms of , and we need to find the value for , i.e. just . We can do this easily by dividing both sides of the equation by .

Rounded to the nearest percent, our answer is that is approximately 93% of .

Bringing it all together: question walkthrough video

If you’d like some additional explanation. here’s a video walkthrough of a percent change problem:

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