GRE Data Interpretation: Algebra Questions

Most GRE Data Interpretation questions are pure arithmetic: read a table, compute a percentage, compare two values. But a small subset demands something different — algebraic reasoning. These questions ask you to set up equations from data, solve for unknowns, or combine fractions weighted by group size. They tend to land at Medium-to-Hard difficulty, and they catch test-takers off guard precisely because the rest of the DI set felt straightforward. Below you will learn the four algebraic patterns that appear, work through two interactive examples step by step, and then practice with six guided questions.

What Are DI Algebra Questions?

Data Interpretation questions appear in sets on the GRE: a shared data display (table, graph, or chart) followed by two to five questions. Most of those questions ask you to read values and do arithmetic. A DI algebra question goes further — it introduces a condition, a hypothetical change, or an unknown variable that requires you to build and solve an algebraic relationship using the displayed data.

The algebra itself is rarely complex. You will not encounter quadratics or systems of three equations. Instead, the challenge is recognizing that you need algebra at all, identifying the right data points to pull from the display, and setting up the equation correctly before computing.

Frequency note: DI + Algebra is one of the rarer GRE combinations. In official practice materials only a handful of DI questions require algebraic reasoning. But when they appear, they tend to be Medium to Hard difficulty — making them high-value targets for your preparation.

Four Algebraic Patterns You'll See

Nearly every DI algebra question falls into one of four patterns. Recognizing the pattern quickly tells you what kind of equation to set up.

Fraction or Proportion with an Unknown

The question introduces fractions that apply to different subgroups from the data display. You must compute each product separately and combine them — a weighted sum, not a simple average of the fractions.

Working Backward from a Result

You are given an outcome (such as a corrected average) and must determine what input change produces it. The setup typically involves the arithmetic mean property: changing one of

n

values by

D

changes the mean by

\frac{D}{n}

Rate of Change as Slope

The question asks for an average rate of change between two data points — which is the algebraic concept of slope. You may also need to extrapolate beyond the displayed range using a linear model.

Equation from Constraints

A condition stated in the question, combined with data from the display, requires setting up and solving a single equation. Examples include solving for an unknown expense rate or finding a break-even point.

How to Solve DI Algebra Step by Step

These five strategies apply across all four patterns. Work through them in order and you will avoid the most common errors.

Identify the unknown first

Before looking at the data, determine what the question is asking you to find. This tells you what your variable represents. If the question asks for a new expense rate, your unknown is r. If it asks for projected enrollment, your unknown is the future value. Naming the unknown first prevents you from pulling irrelevant data.

Extract all needed values from the display

Write down the specific numbers from the table or graph that are relevant to the question. Do not try to hold them in working memory. For example, if the question involves two departments, pull the values for both departments before computing anything.

Set up the relationship before computing

Write the equation or formula in terms of the values you have extracted. For instance, write

P = S(1 - r) - F

before plugging in numbers. This helps prevent errors from premature arithmetic and makes it easier to check your work.

Watch for weighted combinations

When combining fractions or proportions from different groups, you must weight by group size, not simply average the fractions. If

\frac{1}{3}

of 42 people and

\frac{2}{9}

of 45 people satisfy a condition, compute

14 + 10 = 24

out of 87 total — do not average

\frac{1}{3}

and

\frac{2}{9}

Simplify before computing

Factor or cancel terms to avoid unnecessary large-number arithmetic. Many DI algebra setups have terms that cancel — for example, when a data correction changes the mean, the original sum cancels and you only need the change divided by the count.

Pro tip: If you find yourself doing heavy arithmetic with five-digit numbers, step back. GRE DI algebra questions are designed so that terms cancel or simplify. Look for the shortcut before grinding through the calculation.

Worked Example: Weighted Fractions

Work through each step below. You must answer each mini-challenge correctly to unlock the next step. If you get stuck, a second wrong attempt will reveal the answer so you can keep going.

Interactive Walkthrough0/7 steps

Weighted Fractions from a Data Display

Two pie charts show the distribution of faculty at College X. There are 200 adjunct faculty and 250 non-adjunct faculty. Biological Sciences accounts for 5% of adjunct and 10% of non-adjunct. Health Sciences accounts for 16% of adjunct and 8% of non-adjunct.

For the biological sciences and health sciences faculty combined,

\frac{1}{3}

of the adjunct faculty and

\frac{2}{9}

of the non-adjunct faculty are medical doctors. What fraction of all the faculty in those two fields combined are medical doctors?

Step 1: Identify the relevant adjunct percentage

What percentage of adjunct faculty are in Bio + Health combined? (5% + 16%)

Step 2: Count the adjunct faculty in these fields

Step 3: Count non-adjunct faculty in these fields

Step 4: Apply the first fraction

Step 5: Apply the second fraction

Step 6: Form the combined fraction

Step 7: Simplify the fraction

Worked Example: How a Data Correction Changes the Mean

This example teaches the algebraic shortcut for data-correction questions. Work through each step to see why you never need the original sum.

Interactive Walkthrough0/5 steps

Algebraic Impact of a Data Correction

A line graph shows the value of imports for Country Z from 2000 to 2009 (10 years). The 2007 value reads approximately $7 billion. You are told the 2007 value should have been $5 billion instead.

If the value of imports for 2007 were corrected, approximately how much less would the 10-year average (arithmetic mean) have been?

Step 1: Find the change in the single data point

The 2007 value drops from $7 billion to $5 billion. By how many billion does it decrease?

Step 2: Count the data points

Step 3: Recall the key formula

Step 4: Apply the formula

Step 5: Convert units to match the answer choices

Practice Questions

Now apply what you learned. Each question has a step-by-step solution walkthrough — after you submit your answer, click through the solution one step at a time to compare against your own work.

PharmaCo Inc. — Quarterly Sales and Expenses

Quarterly Sales Revenue and Expense Structure for Five Regions of PharmaCo Inc., Fiscal Year 2023

Region	Q1 ($M)	Q2 ($M)	Q3 ($M)	Q4 ($M)	Fixed Exp. ($M/yr)	Var. Rate (% Sales)
Northeast	$24	$28	$32	$36	$15	30%
Southeast	$18	$20	$22	$24	$10	35%
Midwest	$30	$27	$33	$30	$20	25%
West	$40	$44	$48	$52	$25	20%
International	$15	$18	$21	$24	$12	40%

Question 1 — Linear Extrapolation

The Northeast region's quarterly sales increased at a constant rate from Q1 through Q4 of fiscal year 2023. If this linear trend continued at the same constant quarterly rate, what would the projected sales be for Q2 of fiscal year 2024, in millions of dollars?

Question 2 — Equation from Constraints

The Southeast region's annual profit equals total annual sales minus total annual expenses (fixed expenses plus variable expense rate times total annual sales). If the variable expense rate were reduced so that annual profit equaled exactly $53 million, with fixed expenses unchanged, what would the new variable expense rate be?

Question 3 — Data Correction and the Mean

If the Midwest region's Q3 sales figure of $33 million were discovered to have been recorded incorrectly and should have been $27 million, by how many million dollars would the Midwest region's average quarterly sales decrease?

Westfield University — Research Funding and Staffing

Annual Research Funding and Staffing by Department at Westfield University, 2019-2023

Department	2019 ($M)	2020 ($M)	2021 ($M)	2022 ($M)	2023 ($M)	Researchers (2023)
Biology	$4.0	$4.8	$5.6	$6.4	$7.2	45
Chemistry	$3.5	$3.8	$4.1	$4.4	$4.7	30
Physics	$5.0	$5.5	$5.0	$6.0	$6.5	35
Computer Science	$2.0	$3.0	$4.5	$6.0	$8.0	50
Engineering	$6.0	$6.2	$6.8	$7.0	$7.5	40

Question 4 — Weighted Fractions

\frac{2}{5}

of the Biology department's researchers and

\frac{1}{3}

of the Chemistry department's researchers hold joint appointments, what fraction of all researchers in those two departments combined hold joint appointments?

Riverside College — Enrollment and Tuition

Annual Student Enrollment and Tuition Data for Five Academic Programs at Riverside College, 2019-2023

Program	2019	2020	2021	2022	2023	Tuition ($K/yr)
Nursing	200	240	280	320	360	$12
Business	350	340	330	320	310	$10
Eng. Technology	150	180	210	240	270	$14
Liberal Arts	400	380	360	340	320	$8
Computer Science	100	150	200	250	300	$11

Question 5 — Linear Model Slope

The Computer Science program's enrollment can be modeled by the linear equation

E(t) = mt + b

, where

t

is the number of years after 2019 and

E

is the enrollment. Based on the data from 2019 to 2023, what is the value of

m

Question 6 — Weighted Fractions (variant)

\frac{1}{4}

of the Nursing program's students and

\frac{1}{6}

of the Engineering Technology program's students in 2023 are enrolled on a part-time basis, what fraction of the combined students from these two programs are part-time?

Three Common Traps

Trap 1 — Applying a fraction to the wrong group. When a question says "

\frac{1}{3}

of group A and

\frac{2}{9}

of group B," you must compute each product separately and then combine. Applying a single fraction to the combined total, or averaging the two fractions without weighting by group size, gives a wrong answer every time.

Trap 2 — Confusing total change with average change. The total change from Q1 to Q4 is a single number. The average rate of change per quarter divides that total by the number of intervals (3, not 4, since there are 3 intervals between 4 data points). Dividing by the wrong count shifts your answer by one distractor.

Trap 3 — Forgetting to divide by the number of items. When a question asks how an average changes if one data point is corrected, the change in the average is the change in the single value divided by the total count of items. Reporting the raw difference instead of the change in the mean is the most frequent error on these questions.

When Does a DI Question Need Algebra?

Not every DI question that involves computation is algebraic. Use this table to distinguish arithmetic DI from algebraic DI at a glance.

Situation	Domain	Why
What percent of total X is Y?	Arithmetic	Direct computation from displayed values
What is the ratio of A to B?	Arithmetic	Direct division of displayed values
If $\frac{1}{3}$ of group A and $\frac{2}{9}$ of group B are doctors, what fraction of all are doctors?	Algebra	Must set up a weighted expression combining displayed values with given fractions
If the 2007 value were corrected to $5B, how would the average change?	Algebra	Must reason abstractly about how changing one value affects a mean
At this rate of change, what would the value be in 2022?	Algebra	Must compute a slope and extrapolate using a linear model
What was the percent change from 2014 to 2016?	Arithmetic	Direct application of the percent change formula

The key indicator of algebra in DI is the introduction of an unknown or a hypothetical condition that requires you to set up and solve a relationship, rather than simply reading and computing from displayed values.

Study Checklist

DI Algebra Mastery Checklist0/8 complete

Frequently Asked Questions

How often do algebra-based Data Interpretation questions appear on the GRE?

DI Algebra is one of the less common combinations on the GRE. Most Data Interpretation questions are solvable with arithmetic and data analysis alone. However, the algebraic DI questions that do appear tend to be rated Medium to Hard difficulty, so preparation is worthwhile. Expect zero to two such questions per test.

What is the difference between a DI algebra question and a regular algebra question?

In a standalone algebra question you are given an equation and asked to solve it. In a DI algebra question you must extract numerical values from a data display — a table, graph, or chart — and then set up the algebraic relationship yourself. The algebra is typically one or two steps, but the challenge lies in identifying which data points to use and how they relate.

How do I know when a DI question requires algebra instead of arithmetic?

The key indicator is the introduction of an unknown or a hypothetical condition. If the question asks you to set up and solve a relationship rather than simply reading and computing from displayed values, it requires algebra. Look for phrases like "if the value were corrected," "what fraction of the combined group," or "at this rate of change."

Do I need to memorize formulas for DI algebra questions?

No special formulas are required beyond the basics you already know: slope = $\frac{\Delta y}{\Delta x}$ , arithmetic mean = $\frac{\text{sum}}{\text{count}}$ , and profit = revenue minus cost. The key skill is translating a word problem with data into one of these relationships.

What is the most common mistake on DI algebra questions?

The most common mistake is applying a fraction to the wrong group. When a question says "1/3 of group A and 2/9 of group B," you must compute each product separately and then combine. Averaging the fractions without weighting by group size gives a wrong answer. A close second is forgetting to divide by the count when a data correction changes the mean.