SAT Math: Percentages

Percentages: percent change and reverse percentages.

Problem-Solving and Data Analysis · Percentages
Both modules
12 practice questions · 3 with free solutions
Calculator allowed (Desmos)

Practise percentages →Adaptive SAT module

What the test covers

Percent change, successive changes, reverse percentages

Key ideas

An increase of $p %$ multiplies by $1 + \frac{p}{100}$ ; a decrease multiplies by $1 - \frac{p}{100}$ .
Successive changes multiply: $+ 30 %$ then $- 30 %$ gives $1.3 \times 0.7 = 0.91$ , a 9% decrease.
Original value = new value $\div$ multiplier.

Common mistakes

Taking 20% off the new price does not undo a 20% increase.
'Percent of' and 'percent more than' are different.

Do it in Desmos

Type the multiplier chain into the calculator in one line to avoid rounding.

Worked example

After a 20% increase, the price of a jacket is $66. What was the price, in dollars, before the increase?

$60$
$46$
$55$
$52.8$

Answer: C: $55$

$1.2 p = 66$ , $p = 55$ . (Taking 20% off $66 gives $52.80, which is not the same.)

Practice questions

Try each question before opening the solution. Desmos or your own calculator is allowed on every SAT Math question. Solutions to the first 2 are open to everyone; the rest need only a free account. Every answer here was checked independently before it was published.

Question 1

After a 20% increase, the price of a coat is $144. What was the price, in dollars, before the increase?

$120$
$\frac{648}{5}$
$\frac{576}{5}$
$124$

Show the answer and solution

Answer: A: $120$

$1.2 p = 144$ , so $p = 120$ . (Taking 20% off $144 gives a different number.)

Question 2

A quantity is increased by 30% and the result is then decreased by 30%. The final value is $p$ % less than the original value. What is $p$ ?

Student-produced response: type your answer.

Show the answer and solution

Answer: 9

$1.3 \times 0.7 = 0.91$ , so the final value is 91% of the original: 9% less.

Question 3

After a 40% increase, the price of a coat is $168. What was the price, in dollars, before the increase?

$128$
$\frac{672}{5}$
$\frac{504}{5}$
$120$