Percentages · SAT · Courselo

Lesson 2 of 6 · Problem-solving and data analysis

Percentages

6 min read · about 1 h with practice3 quick checks≈2% of the testFoundational

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Percent questions are some of the most dependable points in SAT Math. Almost every one gives way to a single habit: turn each percent into a multiplier. Expect one or two direct percent questions per test, in either module and as multiple choice or student-produced response (SPR). Percent reasoning also turns up inside survey tables, data displays and exponential growth models.

By the end you’ll be able to

Compute a percent of a quantity and express one quantity as a percent of another
Compute percent increase and decrease, and find an original value from a changed value
Chain successive percent changes with multipliers
Distinguish percentage points from percent change

What the exam asks

Problem-Solving and Data Analysis accounts for about 15% of the Math section (5–7 of the 44 scored questions). Percent items come in a few forms:

Percent of a quantity: “What is 35% of 240?” or “18 is what percent of 75?”
Percent change: find the new value after an increase or decrease, or the percent change between two values.
Reverse percent: you are given the value after a change and asked for the original.
Successive changes: a markup then a discount, a discount then sales tax, or a rise then a fall.
Percents with different bases: “60% of students take a science elective; of those, 35% take chemistry.”
Wording traps (hard): “ $a$ is 70% less than $b$ ,” “300% of $n$ ” versus “300% more than $n$ ,” and percentage points versus percent change.

Check your understanding

3 questions on percentages. Every option is explained once you answer.

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Flashcards

The first 3 of 10 cards for this topic. Sign in and finish the lesson to review them with spaced repetition.

PromptCard 1 of 3

What is the multiplier for an increase of $r\%$ ? Give an example.

Words	Math
$p\%$ of $x$	$\frac{p}{100}x$
$x$ is what percent of $y$ ?	$\frac{x}{y} \times 100$
$p\%$ more than $x$ (increase by $p\%$ )	$\left(1 + \frac{p}{100}\right)x$
$p\%$ less than $x$ (decrease by $p\%$ )	$\left(1 - \frac{p}{100}\right)x$

Change	Multiplier
Increase by 15%	$\times 1.15$
Decrease by 15%	$\times 0.85$
Increase by 100% (doubling)	$\times 2$
250% of	$\times 2.5$
250% more than	$\times 3.5$
Decrease by 4%	$\times 0.96$

Percentages

By the end you’ll be able to

What the exam asks

Check your understanding

Flashcards

Core ideas

Translate the words into math

Multipliers

Percent change

Reverse percent

Successive changes multiply

Percentage points versus percent

Worked examples

Exam technique

Common mistakes

Quick recap

By the end you’ll be able to

What the exam asks

vii.Check your understanding

viii.Flashcards

Core ideas

Translate the words into math

Multipliers

Percent change

Reverse percent

Successive changes multiply

Percentage points versus percent

Worked examples

Exam technique

Common mistakes

Quick recap

Check your understanding

Flashcards