SAT Math: Percentages

Percentages: percent change and reverse percentages.

Problem-Solving and Data Analysis · Percentages
Both modules
12 practice questions
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 $1+\tfrac p{100}$; a decrease multiplies by $1-\tfrac p{100}$.
Successive changes multiply: $+30\%$ then $-30\%$ gives $1.3\times0.7=0.91$, 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: $55$

$1.2p=66$, $p=55$. (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. Every answer here was re-checked independently by computer before it was published.

Question 1

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

$1.3\times0.7=0.91$, so the final value is 91% of the original: 9% less.

Question 2

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

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

Show the answer and solution

Answer: D: $120$

$1.4p=168$, so $p=120$. (Taking 40% off $168 gives a different number.)

Question 3

After a 30% increase, the price of a coat is $65. What was the price, in dollars, before the increase?

$50$
$\frac{91}{2}$
$\frac{221}{4}$
$35$

Show the answer and solution

Answer: A: $50$

$1.3p=65$, so $p=50$. (Taking 30% off $65 gives a different number.)

Question 4

After a 30% increase, the price of a coat is $104. What was the price, in dollars, before the increase?

$\frac{364}{5}$
$80$
$\frac{442}{5}$
$74$

Show the answer and solution

Answer: B: $80$

$1.3p=104$, so $p=80$. (Taking 30% off $104 gives a different number.)

Question 5

After a 30% increase, the price of a coat is $78. What was the price, in dollars, before the increase?

$\frac{273}{5}$
$48$
$\frac{663}{10}$
$60$

Show the answer and solution

Answer: D: $60$

$1.3p=78$, so $p=60$. (Taking 30% off $78 gives a different number.)

Question 6

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: $120$

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

Question 7

A quantity is increased by 30% and the result is then decreased by 50%. 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: 35

$1.3\times0.5=0.65$, so the final value is $65\%$ of the original: $35\%$ less.

Question 8

A quantity is increased by 30% and the result is then decreased by 40%. 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: 22

$1.3\times0.6=0.78$, so the final value is $78\%$ of the original: $22\%$ less.

Question 9

A quantity is increased by 25% and the result is then decreased by 40%. 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: 25

$1.25\times0.6=0.75$, so the final value is $75\%$ of the original: $25\%$ less.

Question 10

A quantity is increased by 10% and the result is then decreased by 20%. 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: 12

$1.1\times0.8=0.88$, so the final value is $88\%$ of the original: $12\%$ less.

Question 11

A quantity is increased by 50% and the result is then decreased by 50%. 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: 25

$1.5\times0.5=0.75$, so the final value is $75\%$ of the original: $25\%$ less.

Keep going

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