How do I calculate percent change on a GRE Data Interpretation question?

Subtract the original value from the new value, divide by the original value, and multiply by 100%. The most common mistake is dividing by the new value — always use the starting amount as the denominator.

What is the difference between percentage points and percent change?

Percentage points measure the raw gap between two percentages, so a move from 40% to 44% is 4 points. Percent change measures that gap relative to the starting percentage, so the same move is a 4/40 = 10% relative increase. GRE distractors deliberately swap the two.

Why do GRE Data Interpretation questions come in sets?

A DI set attaches several questions to one figure so it can test whether you can extract different quantities from the same table or graph. Read the figure and its units carefully once, and that understanding pays off across every question in the set.

How do I avoid unit mistakes in Data Interpretation?

Read the caption before you answer. If a table is labeled "in thousands of dollars," an entry of 48 means \$48,000, so multiply by 1,000 whenever the question asks for an answer in dollars rather than in thousands.

CramClub

Data Interpretation

Read GRE bar graphs, line graphs, tables, and pie charts, then answer multi-step percent and ratio questions from a shared data set.

GREquantitative reasoningmedium18 min read6 worked examples6 practice

Key Formulas

Percent change

$\dfrac{\text{new} - \text{old}}{\text{old}} \times 100\%$

Always divide by the original value.

Share of total

$\dfrac{\text{part}}{\text{whole}} \times 100\%$

What fraction one category is of the whole.

Average (mean)

$\dfrac{\text{sum of values}}{\text{number of values}}$

Sum a row or column, then divide by the count.

Percentage points vs. percent

points $= p_2 - p_1$ ; percent change $= \dfrac{p_2 - p_1}{p_1}$

A shift from 25% to 30% is 5 points but a 20% relative increase.

Video Lesson

Explanation

What a Data Interpretation Set Is

A Data Interpretation (DI) set presents one figure — a table, bar graph, line graph, or pie chart — followed by several questions that all read from the same figure. On the GRE these questions cluster together, so the payoff for reading the figure carefully once is large: you reuse that understanding across the whole set. The math itself is percents, ratios, averages, and the occasional probability, but the difficulty lives in extracting the right numbers and chaining several steps without a slip.

The Master Figure for This Lesson

Every worked example and practice item below reads from this one table. Treat it the way you would a real GRE DI set: study it once, then answer.

Monthly revenue (in thousands of dollars) at GreenLeaf Café, by location

Month	Downtown	Riverside	Airport	Total
January	48	30	42	120
February	54	36	30	120
March	60	45	45	150
April	66	39	45	150

All amounts are in thousands of dollars. For instance, Downtown earned $48{,}000 in January.

Reading the Figure Correctly

Three habits prevent most DI errors:

Check the units. Here every entry is thousands of dollars, so " $48$ " means $48{,}000. Answers may be requested in dollars, thousands, or percentages.
Know your row from your column. Read across a row for one month across locations; read down a column for one location across months.
Use the totals. The Total column is the sum across the three locations — handy for share and percentage questions, and a quick way to check your own arithmetic.

Percent Change

A staple DI computation is percent change from an old value to a new value:

$\text{percent change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100\%$

Downtown revenue rose from $48{,}000 in January to $54{,}000 in February, a change of $\dfrac{54 - 48}{48} \times 100\% = \dfrac{6}{48} \times 100\% = 12.5\%$ . Always divide by the original value, not the new one.

Percent of a Total (Share)

To find what fraction one part contributes to a whole, divide the part by the total:

$\text{share} = \frac{\text{part}}{\text{whole}} \times 100\%$

In March, Riverside earned $45{,}000 of the $150{,}000 total, a share of $\dfrac{45}{150} = 30\%$ .

Ratios Between Categories

DI questions love ratios. In April, the ratio of Downtown to Riverside revenue is $66 : 39$ . Divide both by their common factor $3$ to simplify: $22 : 13$ . Keep the order the question asks for — " $A$ to $B$ " is not " $B$ to $A$ ."

Averages Across a Row or Column

The average (arithmetic mean) is the sum divided by the count. Airport's average monthly revenue over the four months is

$\frac{42 + 30 + 45 + 45}{4} = \frac{162}{4} = 40.5 \ (\text{thousand dollars}) = \dollar 40{,}500.$

Multi-Step Chaining

The hardest DI questions stack two or three of these operations. For example: "By what percent did Airport's share of monthly revenue change from January to February?" You must compute Airport's January share ( $42/120 = 35\%$ ), its February share ( $30/120 = 25\%$ ), and then the change ( $25\% - 35\% = -10$ percentage points, a drop). Note the difference between a change in percentage points and a percent change — GRE distractors exploit exactly this confusion.

A Reliable Game Plan

Read units and headers once, before touching any question.
Percent change? Difference over the original, times $100\%$ .
Share of total? Part over whole.
Ratio? Simplify by the common factor; keep the requested order.
"Percentage points" vs. "percent"? Points is a subtraction of two percentages; percent change divides by the original.

Worked Examples

— follow the steps, hardest last

Read a single cell

easy

Using the GreenLeaf table, how much revenue did Riverside earn in February, in dollars?

Percent change

medium

By what percent did Downtown revenue increase from January to March?

Share of the total

medium

In April, what percent of total revenue came from the Airport location?

Ratio between two categories

medium

In January, what is the ratio of Downtown revenue to Airport revenue, in lowest terms?

Average across a column

hard

What is the average (arithmetic mean) monthly revenue for Riverside over the four months, in dollars?

Multi-step — change in share

hard

By how many percentage points did Airport's share of monthly total revenue change from January to February?

Watch Out For

Dividing percent change by the new value instead of the original, e.g. computing $\tfrac{60 - 48}{60}$ for a rise from 48 to 60.
Percent change always divides by the ORIGINAL value: $\tfrac{60 - 48}{48} = 25\%$ , not $\tfrac{12}{60} = 20\%$ .
Ignoring the units line, so an answer of "36" is reported as $36 instead of $36{,}000.
Read the units caption before answering. Here every entry is in thousands, so multiply by 1{,}000 when the question asks for dollars.
Confusing a change in percentage points with a percent change — reporting a shift from 35% to 25% as a "10% decrease."
A move of 10 percentage points is a relative change of $\tfrac{10}{35} \approx 28.6\%$ . Match the wording: "points" means subtract; "percent change" means divide by the original share.
Reversing the order of a ratio, giving $7 : 8$ when the question asks for Downtown to Airport.
Write the ratio in exactly the order named in the question, then simplify. " $A$ to $B$ " puts $A$ first.

Practice Problems

Using the GreenLeaf table (revenue in thousands: Jan Downtown 48, Riverside 30, Airport 42; Feb Downtown 54, Riverside 36, Airport 30), by what percent did Riverside revenue increase from January to February?

Using the GreenLeaf table (March totals: Downtown 60, Riverside 45, Airport 45, Total 150), what percent of March revenue came from the Downtown location?

Using the GreenLeaf table, the Airport location earned 42, 30, 45, and 45 (thousands) in January through April.

Quantity A: Airport's average (arithmetic mean) monthly revenue over the four months Quantity B: $40{,}000

Using the GreenLeaf table (April: Downtown 66, Riverside 39), what is the ratio of Downtown to Riverside revenue in April, in lowest terms?

Using the GreenLeaf table, total monthly revenue was 120 in January and 150 in March (thousands). By what percent did total monthly revenue increase from January to March?

Using the GreenLeaf table, Downtown's share of the monthly total was 48 of 120 in January and 66 of 150 in April. By how many percentage points did Downtown's share of monthly total revenue change from January to April?

Frequently Asked Questions

How do I calculate percent change on a GRE Data Interpretation question?: Subtract the original value from the new value, divide by the original value, and multiply by 100%. The most common mistake is dividing by the new value — always use the starting amount as the denominator.
What is the difference between percentage points and percent change?: Percentage points measure the raw gap between two percentages, so a move from 40% to 44% is 4 points. Percent change measures that gap relative to the starting percentage, so the same move is a 4/40 = 10% relative increase. GRE distractors deliberately swap the two.
Why do GRE Data Interpretation questions come in sets?: A DI set attaches several questions to one figure so it can test whether you can extract different quantities from the same table or graph. Read the figure and its units carefully once, and that understanding pays off across every question in the set.
How do I avoid unit mistakes in Data Interpretation?: Read the caption before you answer. If a table is labeled "in thousands of dollars," an entry of 48 means \$48,000, so multiply by 1,000 whenever the question asks for an answer in dollars rather than in thousands.

Keep Going

Fractions, Decimals, and Percents

Move fluently among fractions, decimals, and percents, and master the GRE’s favorite traps: percent of a number, percent increase and decrease, successive percent changes, and "percent more/less than."

Descriptive Statistics

Master mean, median, mode, range, quartiles, weighted averages, and standard deviation as a spread measure for GRE Quant data-analysis questions.

Probability

Master GRE probability — complements, the addition and multiplication rules, "at least one" via complement, conditional probability, and geometric probability.

Ready to test yourself?

Put this skill to work on a full-length adaptive practice test.

Data Interpretation

Read GRE bar graphs, line graphs, tables, and pie charts, then answer multi-step percent and ratio questions from a shared data set.

GREquantitative reasoningmedium18 min read6 worked examples6 practice

Key Formulas

Percent change

$\dfrac{\text{new} - \text{old}}{\text{old}} \times 100\%$

Always divide by the original value.

Share of total

$\dfrac{\text{part}}{\text{whole}} \times 100\%$

What fraction one category is of the whole.

Average (mean)

$\dfrac{\text{sum of values}}{\text{number of values}}$

Sum a row or column, then divide by the count.

Percentage points vs. percent

points $= p_2 - p_1$ ; percent change $= \dfrac{p_2 - p_1}{p_1}$

A shift from 25% to 30% is 5 points but a 20% relative increase.

Video Lesson

Explanation

What a Data Interpretation Set Is

The Master Figure for This Lesson

Every worked example and practice item below reads from this one table. Treat it the way you would a real GRE DI set: study it once, then answer.

Monthly revenue (in thousands of dollars) at GreenLeaf Café, by location

Month	Downtown	Riverside	Airport	Total
January	48	30	42	120
February	54	36	30	120
March	60	45	45	150
April	66	39	45	150

All amounts are in thousands of dollars. For instance, Downtown earned $48{,}000 in January.

Reading the Figure Correctly

Three habits prevent most DI errors:

Check the units. Here every entry is thousands of dollars, so " $48$ " means $48{,}000. Answers may be requested in dollars, thousands, or percentages.
Know your row from your column. Read across a row for one month across locations; read down a column for one location across months.
Use the totals. The Total column is the sum across the three locations — handy for share and percentage questions, and a quick way to check your own arithmetic.

Percent Change

A staple DI computation is percent change from an old value to a new value:

$\text{percent change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100\%$

Percent of a Total (Share)

To find what fraction one part contributes to a whole, divide the part by the total:

$\text{share} = \frac{\text{part}}{\text{whole}} \times 100\%$

In March, Riverside earned $45{,}000 of the $150{,}000 total, a share of $\dfrac{45}{150} = 30\%$ .

Ratios Between Categories

Averages Across a Row or Column

The average (arithmetic mean) is the sum divided by the count. Airport's average monthly revenue over the four months is

$\frac{42 + 30 + 45 + 45}{4} = \frac{162}{4} = 40.5 \ (\text{thousand dollars}) = \dollar 40{,}500.$

Multi-Step Chaining

A Reliable Game Plan

Read units and headers once, before touching any question.
Percent change? Difference over the original, times $100\%$ .
Share of total? Part over whole.
Ratio? Simplify by the common factor; keep the requested order.
"Percentage points" vs. "percent"? Points is a subtraction of two percentages; percent change divides by the original.

Worked Examples

— follow the steps, hardest last

Read a single cell

easy

Using the GreenLeaf table, how much revenue did Riverside earn in February, in dollars?

Percent change

medium

By what percent did Downtown revenue increase from January to March?

Share of the total

medium

In April, what percent of total revenue came from the Airport location?

Ratio between two categories

medium

In January, what is the ratio of Downtown revenue to Airport revenue, in lowest terms?

Average across a column

hard

What is the average (arithmetic mean) monthly revenue for Riverside over the four months, in dollars?

Multi-step — change in share

hard

By how many percentage points did Airport's share of monthly total revenue change from January to February?

Watch Out For

Dividing percent change by the new value instead of the original, e.g. computing $\tfrac{60 - 48}{60}$ for a rise from 48 to 60.
Percent change always divides by the ORIGINAL value: $\tfrac{60 - 48}{48} = 25\%$ , not $\tfrac{12}{60} = 20\%$ .
Ignoring the units line, so an answer of "36" is reported as $36 instead of $36{,}000.
Read the units caption before answering. Here every entry is in thousands, so multiply by 1{,}000 when the question asks for dollars.
Confusing a change in percentage points with a percent change — reporting a shift from 35% to 25% as a "10% decrease."
A move of 10 percentage points is a relative change of $\tfrac{10}{35} \approx 28.6\%$ . Match the wording: "points" means subtract; "percent change" means divide by the original share.
Reversing the order of a ratio, giving $7 : 8$ when the question asks for Downtown to Airport.
Write the ratio in exactly the order named in the question, then simplify. " $A$ to $B$ " puts $A$ first.

Practice Problems

Using the GreenLeaf table (March totals: Downtown 60, Riverside 45, Airport 45, Total 150), what percent of March revenue came from the Downtown location?

Using the GreenLeaf table, the Airport location earned 42, 30, 45, and 45 (thousands) in January through April.

Quantity A: Airport's average (arithmetic mean) monthly revenue over the four months Quantity B: $40{,}000

Using the GreenLeaf table (April: Downtown 66, Riverside 39), what is the ratio of Downtown to Riverside revenue in April, in lowest terms?

Using the GreenLeaf table, total monthly revenue was 120 in January and 150 in March (thousands). By what percent did total monthly revenue increase from January to March?

Frequently Asked Questions

How do I calculate percent change on a GRE Data Interpretation question?: Subtract the original value from the new value, divide by the original value, and multiply by 100%. The most common mistake is dividing by the new value — always use the starting amount as the denominator.
What is the difference between percentage points and percent change?: Percentage points measure the raw gap between two percentages, so a move from 40% to 44% is 4 points. Percent change measures that gap relative to the starting percentage, so the same move is a 4/40 = 10% relative increase. GRE distractors deliberately swap the two.
Why do GRE Data Interpretation questions come in sets?: A DI set attaches several questions to one figure so it can test whether you can extract different quantities from the same table or graph. Read the figure and its units carefully once, and that understanding pays off across every question in the set.
How do I avoid unit mistakes in Data Interpretation?: Read the caption before you answer. If a table is labeled "in thousands of dollars," an entry of 48 means \$48,000, so multiply by 1,000 whenever the question asks for an answer in dollars rather than in thousands.

Keep Going

Fractions, Decimals, and Percents

Descriptive Statistics

Master mean, median, mode, range, quartiles, weighted averages, and standard deviation as a spread measure for GRE Quant data-analysis questions.

Probability

Master GRE probability — complements, the addition and multiplication rules, "at least one" via complement, conditional probability, and geometric probability.

Ready to test yourself?

Put this skill to work on a full-length adaptive practice test.