GRE Percent Change: Formulas, Comparisons, and Worked Examples

Percent change questions test a small set of ideas in ways that expose rushed reading. The arithmetic is usually manageable. The hard part is identifying the starting value, choosing the denominator, keeping units consistent, and answering the comparison the prompt actually asks. A reliable setup prevents most errors: name the original value, name the new value, subtract to find the change, divide by the original, and convert the resulting ratio to a percent.

The percent change formula

If a quantity moves from A to B, its percent change is (B − A) ÷ A × 100%. A is the original or baseline amount. B is the amount after the change. If B is greater than A, the result is positive and describes an increase. If B is smaller, the result is negative and describes a decrease. When the question asks for the size of the decrease, report the positive magnitude and label it a decrease.

For example, a subscription rises from $40 to $50. The change is $10, and $10 ÷ $40 = 0.25, so the price increased by 25%. Dividing by $50 would answer a different question: the increase is 20% of the final price. Percent change uses the starting amount because it measures the change relative to where the quantity began.

Before calculating, turn the sentence into an equation. ‘By what percent did the value rise from 80 to 92?’ means (92 − 80) ÷ 80. ‘The value 12 is what percent of 92?’ means 12 ÷ 92. Those happen to use the same difference but different denominators. Underline words such as from, to, of, increase, decrease, and points.

A dependable four-step setup

1. Label the starting amount as the original value and the ending amount as the new value.
2. Subtract in the order new minus original so the sign shows direction.
3. Divide by the original value, not by the new value or the size of the change.
4. Multiply by 100% and state whether the result is an increase or a decrease.

Keep the original unit on both values while subtracting. If a town grows from 8 thousand residents to 10 thousand, its increase is 2 thousand. The ratio (2 thousand)/(8 thousand) is 0.25 because the units cancel. The growth is 25%. If one entry is given in thousands and another as an absolute count, first put them in the same unit.

Worked example: increase versus final value

A lab processes 240 samples in one week and 300 in the next. What is the percent increase? The difference is 60 samples. Divide by the original 240: 60/240 = 1/4 = 25%. The second week's volume is 125% of the first week's volume; that is not the percent increase. The increase itself is 25%.

A useful check is to reconstruct the new value. Twenty-five percent of 240 is 60. Adding that increase gives 300, exactly the stated ending value. If you had answered 20%, then 20% of 240 would be 48, producing 288 rather than 300. This reverse check catches a denominator mistake quickly.

Percent decrease

The same formula works when a quantity falls. A jacket marked down from $120 to $90 falls by $30. Divide $30 by the original $120 to get 0.25, or a 25% decrease. The sale price is 75% of the original price. Those statements are equivalent, but only the first describes the percentage decrease.

Do not use the lower amount as the base merely because it appears last in the sentence. The question ‘$90 is what percent less than $120?’ still uses $120 as the baseline. By contrast, ‘$30 is what percent of $90?’ has $90 as the named whole. Parse the relationship rather than relying on sentence order.

Percentage points and relative percent change

When a percentage rate changes, distinguish a percentage-point difference from a percent change in the rate. If an approval rate moves from 40% to 50%, it rises by 10 percentage points. Relative to its starting rate, the increase is 10/40 = 25%. The first compares two percentage values by subtraction; the second divides that difference by the starting percentage.

A question asking ‘how many percentage points?’ calls for subtraction only. A question asking ‘what percent increase?’ calls for subtraction followed by division by the original rate. The units are different: percentage points are points on the percent scale, while the relative change is a percent of the old rate.

Successive percentage changes

Apply each percentage change to the amount that exists at that stage. Suppose a $200 item rises by 10% and then falls by 10%. The increase is $20, giving $220. The decrease is 10% of $220, or $22. The final amount is $198, a net decline of $2 or 1% of the initial $200. Equal percentage increase and decrease do not cancel because their bases differ.

For a compact calculation, multiply by a factor. Increase by 10% means multiply by 1.10. Decrease by 10% means multiply by 0.90. The combined factor is 1.10 × 0.90 = 0.99, so the final value is 99% of the starting value. This method is especially useful when a question includes several consecutive changes.

A 20% increase followed by another 20% increase has factor 1.20 × 1.20 = 1.44, or a total increase of 44%, not 40%. Starting at 100 makes the same point: 100 becomes 120, then 144. When percentages compound, adding rates is generally wrong unless each rate is explicitly calculated on the same original base.

Reverse percentage questions

Sometimes you know the ending value and the percentage change but need the original. If an amount after a 25% increase is 150, then 150 is 125% of the original. Let the original be x: 1.25x = 150, so x = 120. Do not subtract 25% of 150; the increase was calculated from x, not from the ending amount.

For a decrease, an ending value after a 20% reduction is 80% of the original. If the ending value is 96, then 0.80x = 96 and x = 120. The decrease was 24, which is 20% of 120. It is 25% of 96, so adding 20% of the ending amount would not restore the original.

Original GRE-style practice

Question 1: identify the base

A community center increased monthly classes from 48 to 60. The increase is what percent of the original number of classes?

1. 12%
2. 20%
3. 25%
4. 80%

Answer: C, 25%. The increase is 60 − 48 = 12. The question says ‘of the original,’ so divide by 48: 12/48 = 1/4. Choice B results from dividing by the new total, 60, which answers what fraction of the final count the increase represents.

Question 2: compare percentage points

A survey's response rate changes from 32% to 40%. Which statement is correct?

1. The rate rose by 8% and 8 percentage points.
2. The rate rose by 8 percentage points and 25% relative to its original rate.
3. The rate rose by 25 percentage points and 8% relative to its original rate.
4. The rate rose by 20 percentage points and 25% relative to its original rate.

Answer: B. Subtracting gives 40% − 32% = 8 percentage points. The relative increase is 8/32 = 1/4 = 25%. The word ‘and’ matters: one measure is the direct difference between rates, and the other measures that difference against the starting rate.

Question 3: two-step change

A machine produces 500 parts per day. Output increases by 8% and then decreases by 8%. What is the final output?

1. 496.8
2. 500
3. 503.2
4. 540

Answer: A, 496.8. Multiply 500 by 1.08 and then by 0.92: 500 × 1.08 × 0.92 = 496.8. The changes do not cancel because the 8% reduction applies to the larger intermediate output of 540. The net decline is 3.2 parts, or 0.64% of 500.

Question 4: recover the original

After a 15% discount, a backpack costs $102. What was its price before the discount?

1. $117.00
2. $120.00
3. $123.53
4. $135.00

Answer: B, $120. The sale price is 85% of the original, so 0.85x = 102. Dividing by 0.85 gives x = 120. Adding 15% of $102 would produce $117.30, which is wrong because the discount was based on the original price.

Using ratios to simplify arithmetic

Cancel common factors before converting a fraction to a decimal. For an increase from 72 to 90, the change is 18 and 18/72 reduces to 1/4, or 25%. For an increase from 80 to 100, the change is 20 and 20/80 is also 1/4. Recognizing a familiar fraction is faster and less error-prone than long division.

When the values are close to a convenient base, estimate first. An increase from 198 to 220 is 22 on a base near 200, roughly 11%. Exact calculation is 22/198 = 1/9, about 11.1%. Estimation helps reject implausible options, but do not substitute a rough estimate when choices are close or the prompt requests exact comparison.

Reading percent change in tables and graphs

A data display may report counts, rates, or percentage shares. Check the unit and denominator before comparing values. If a department has 15 incidents among 300 employees and another has 20 incidents among 800 employees, the second department has more incidents but a lower rate: 20/800 = 2.5%, compared with 15/300 = 5%. If asked which has the greater increase over time, calculate each group's change using its own starting value.

When values are given in thousands or millions, the scale often cancels in a percent calculation as long as both values use the same scale. A rise from 8 thousand to 10 thousand is 2/8 = 25%. However, a question about the absolute increase still requires the unit: the increase is 2,000, not 2.

For a percentage share, compare numerator and total. A product's share of sales can fall even as its sales rise if the total grows faster. For example, sales might increase from 20 to 24 while all sales rise from 50 to 80. The product's count increased 20%, but its share declined from 40% to 30%. Count change and share change answer different questions.

Common mistakes and how to repair them

• Using the ending amount as the denominator for a change from an original value. Write ‘original’ above the denominator before dividing.
• Reporting the final value as the increase. If the final amount is 125% of the start, the increase is 25%.
• Adding successive rates even though each applies to a different intermediate value. Use multiplication factors instead.
• Confusing percentage points with percent change. Subtract for points; divide by the original rate for relative change.
• Changing the denominator halfway through a calculation. Keep the baseline attached to the question until the answer is stated.
• Dropping a scale such as thousands when the question asks for a count difference. Cancel units only when they appear in both numerator and denominator.

After an error, identify which decision failed. A wrong denominator is a translation error, not an arithmetic error. A correct fraction converted incorrectly is a computation error. A correct 25% calculation described as ‘25 percentage points’ is an interpretation error. Labeling the error points to a useful next drill.

A short practice routine

Begin with ten untimed questions. For every one, write the baseline and the change before calculating. Include at least one decrease, one successive change, one reverse-percentage problem, and one comparison of percentage points. Explain why the denominator is the one you chose. Once the setup is accurate, add time pressure and use estimation to manage the arithmetic.

Review errors the next day without looking at your old solution. Recreate the equation from the wording. If you cannot explain why the denominator is the original amount, return to simple ‘what percent of what?’ questions before adding multistep examples. ETS provides a free mathematics review for foundational concepts; combine it with fresh practice so you learn the reasoning pattern rather than memorize answers.

How percent change fits the GRE

Percentages can appear in quantitative comparisons, word problems, or data interpretation. The current GRE General Test has 27 Quantitative Reasoning questions across two sections, but ETS does not promise a fixed number of percent-change questions. Treat this as a reusable reasoning skill, not a guaranteed topic count. Your result depends on solving the prompt accurately, not on guessing which form of arithmetic will appear.