GMAT® Percents: A Complete Guide

Between tips, tax, sale discounts, loan rates, and the growth numbers in quarterly reports, percents show up often enough that they can seem too familiar to deserve much prep time. If you've been calculating them since school, filing them under "already covered" makes sense.

The exam treats percents less like a topic and more like a language. They show up inside word problems, Data Insights tables and graphs, and interest questions that hinge on one or two conventions rarely taught formally, like which number counts as the "old" value in a percent change. This guide covers what a percent is, the percent-of operation, the percent change formula worth memorizing in one shape, and the simple-versus-compound distinction behind the interest questions.

What a percent is

Take the word apart and it defines itself. Per means "for every," as in three deals per week. Cent means 100, the same cent sitting in century and in 100 cents to a dollar. So a percent is a count for every 100 units, which is just a fraction with 100 as the bottom.

That "for every 100" framing is what makes percents useful for comparing. Saying a company reported $10 million in revenue last year and $12 million this year gives exact quantities, and sometimes exact quantities are what you want. Saying revenue grew 20% gives a different kind of information: for every $100 in last year's revenue, $120 came in this year. The percent version compares the two years on the same scale no matter the company's size, which is part of why reports lean on it.

There's a limit worth knowing about. A percent hides the size of whatever it's describing, so a 90% market share sounds impressive until you learn the market has 20 customers. When a question hands you a percent, the quantities behind it often sit one multiplication away.

Percent of means multiply

When a percent shows up next to the word "of," the word "of" means multiply. Asking for 20% of 10 is asking you to compute:

$\frac{20}{100} \times 10 = 2$

A percent is a fraction over 100, so every percent-of calculation is a multiplication you already know how to set up. For a case with more moving parts, take 38% of 50. Writing the 50 over 1 keeps both factors in fraction form so common factors can cancel:

$\frac{38}{100} \times \frac{50}{1} = \frac{38}{2} = 19$

The 50 cancels against the 100, leaving 38 over 2. Setting the whole number over 1 costs one moment and buys you cancellation instead of long multiplication.

Fractions and decimals are both available, and the question usually makes one of them the fast route. 20% is $\frac{1}{5}$ and 0.2 at the same time; if the other number in the problem divides by 5, the fraction form will cancel something, and if it doesn't, the decimal form is sitting right there. Pick the form that matches the number you were given. Our mental math guide builds the conversion habits that make that pick faster.

The percent change formula

Percent change measures how much a quantity moved, relative to where it started:

$\frac{\text{new} - \text{old}}{\text{old}} \times 100$

We recommend memorizing the formula in one shape, new minus old over old, times 100. The version that circulates as "change over original, times 100" computes the same thing, but under time pressure the word "change" invites slips, like plugging in the new value in the denominator. The new-minus-old version names both numbers, so there's less to reconstruct under time pressure.

Flashcard it if it's not automatic yet. Few formulas on the exam carry as many question types as this one does. (When you see the formula, note what a 100% change means: going up by 100% of the original adds the whole original back, so a 100% increase is a doubling.)

Running it once: what's the percent change from 30 to 60?

$\frac{60 - 30}{30} \times 100 = \frac{30}{30} \times 100 = 100\%$

A 100% increase doubles the value, which the formula just confirmed.

The exam doesn't always announce percent change with those exact words. Phrases like "what percent greater than" and "what percent smaller than" are percent change questions too, and so are percent growth, percent decrease, and similar framings. Don't memorize a phrase list; just associate any claim about something getting bigger or smaller as a percentage with the formula. Writing the formula at the top of your scratch pad when one of these phrases appears is a cheap habit that can prevent common setup errors in these questions.

One rule pins down the setup almost every time: whatever follows the word "than" is the old value. Take "30 is what percent greater than 25?" The 25 follows "than," so 25 is the old value and 30 is the new one:

$\frac{30 - 25}{25} \times 100 = \frac{5}{25} \times 100 = 20\%$

So 30 is 20% greater than 25. Now reverse the wording: "25 is what percent smaller than 30?" The 30 follows "than," so 30 becomes the old value and the denominator changes with it:

$\frac{30 - 25}{30} \times 100 \approx 16.7\%$

Same two numbers, different question: the number that follows "than" sets the denominator.

Successive changes don't cancel

A price rises 20%, then falls 20%. Back where it started? Not quite:

$\$100 \times 1.20 = \$120$

$\$120 \times 0.80 = \$96$

The 20% decrease applies to the new, higher price, so it subtracts $24 instead of the $20 the increase added, and the round trip lands 4% below the start. Percent changes apply to whatever the current value is at the moment they fire, so two changes that look symmetrical almost never cancel. When a question chains them, run them one at a time and let each one use the updated number.

Interest: percent of or percent change

Interest questions are percent questions wearing a finance costume, and the exam's versions come in two flavors. The distinction worth memorizing: if you want the interest itself, that's a percent-of calculation. If you want the total after interest lands, that's a percent change calculation.

Put $100 into an account earning 10% annual interest. The interest is 10% of 100:

$\$100 \times \frac{10}{100} = \$10$

The total in the account after the interest is paid is a different question. The balance went from 100 to some new value, a 10% change, so the new value is 100 plus 10% of the original, or $110. You don't need the percent change formula rearranged for that one; adding the percent to the original does the same work. Answer choices on the exam typically include both the interest amount and the new total, and each is usually the wrong answer to the other question.

Compound interest

Simple interest happens once: $100 earns 10%, the story ends, $110. Compound interest repeats. The account pays the interest, adds it to the balance, and the next round of interest is calculated on the new, larger total, which means interest earning interest.

Compound annually with $100 at 10% for two years. Year one pays 10% of 100, so the balance reaches $110. Year two pays 10% of 110:

$\$110 \times \frac{10}{100} = \$11$

That brings the balance to $121, one dollar more than two rounds of simple interest would have paid, because year two's interest got calculated on a balance that already included year one's interest.

The exam also tests shorter compounding schedules, and the procedure is the same two moves: cut the annual rate by the number of periods, then compound that many times.

Compounded semiannually means twice a year, so cut the annual rate in half and compound it twice. $100 at 10% compounded semiannually pays 5% after six months, growing to $105, then 5% of 105 in the second half:

$\$105 \times 1.05 = \$110.25$

Compounded quarterly means four periods a year, so divide the rate by four and compound four times. $100 at 12% compounded quarterly pays 3% per quarter: $103 after the first quarter, $106.09 after the second, then $109.27, and finally about $112.55 for the year, versus $112.00 that simple interest would have paid.

More periods mean slightly more money, and the exam's problems state the schedule explicitly ("compounded semiannually," "compounded quarterly"), so read the rate line as carefully as the numbers.

Try this one

Try this one before reading on.

Semiannual means two periods, so the 8% annual rate splits into two 4% payments. The first half-year pays 4% of 2,000:

$\$2{,}000 \times 1.04 = \$2{,}080$

The second half-year pays 4% of the new balance:

$\$2{,}080 \times 1.04 = \$2{,}163.20$

The answer is (B). Choice (A) is what simple interest would have paid, one flat 8% with no compounding, and (C) is close to what quarterly compounding would have paid, four 2% periods instead of two 4% ones. Both wrong answers come from reading the schedule differently.

FAQ

What is a percent?

A count for every 100. 20% means 20 out of every 100, which is the fraction $\frac{20}{100}$ and the decimal 0.2. The word itself says it: per (for every) plus cent (100).

How do you calculate a percent of a number?

Multiply the percent, written over 100, by the number. In a question like "20% of 10," the word "of" signals multiplication: $\frac{20}{100} \times 10 = 2$.

What is the percent change formula?

New minus old, divided by old, times 100. Going from 30 to 60 gives $\frac{60 - 30}{30} \times 100 = 100\%$. Whatever follows the word "than" in a percent question is the old value.

What does a 100% increase mean?

The value doubled. A 100% increase adds 100% of the original to itself, leaving two of the original quantity.

Do percent changes cancel out?

No. A 20% increase followed by a 20% decrease nets to 4% below the starting value, because each change applies to the current value, not the original one.

What is the difference between simple and compound interest?

Simple interest is calculated once on the original amount. Compound interest repeats at set intervals, and each round is calculated on the growing balance, so interest earns interest.

How do you calculate semiannual compounding?

Cut the annual interest rate in half and apply it twice a year. $100 at 10% compounded semiannually becomes $105 after six months, then $110.25 after twelve. Quarterly compounding divides the rate by four and applies it four times.

Want to learn even more?

Related reading:

• Translating Percent Word Problems on the GMAT®: A One-Word-at-a-Time System
• GMAT® Percent Word Problems: The Fraction System That Prevents Computation Errors
• GMAT® Weighted Averages: A Complete Guide
• GMAT® Ratios and Proportions: A Complete Guide
• GMAT® Data Sufficiency: How to Approach DS Questions

The Math Basics series rebuilds arithmetic from the ground up, including "GMAT® Focus Edition Math Basics: Percents," which walks the definition, the change formula, and every compounding schedule step by step. Percent change shows up inside the worked problems in Episode 27 of our Real GMAT® Problems series, "Three Systems for Exponents, Primes, and Percent Change". You can hear everything on Spotify, Apple Podcasts, or YouTube.