SAT · SAT Maths
Problem-Solving and Data Analysis
Percentages 7 questions
QUESTION 1 [2 marks]
Easy
What is 35\% of 240?
Show Solution
$0.35\times240=84$.
QUESTION 2 [2 marks]
Easy
A shirt originally priced at \$40 is discounted by 25\%. What is the sale price?
Show Solution
A 25\% discount leaves 75\% of the original price: $40\times0.75=\$30$.
QUESTION 3 [3 marks]
Medium
A town's population increased from 4{,}000 to 4{,}600. What was the percent increase?
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Increase $=4600-4000=600$. Percent increase $=\dfrac{600}{4000}\times100\%=15\%$.
QUESTION 4 [3 marks]
Medium
After a 20\% increase, the price of an item is \$96. What was the original price?
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Let the original price be $x$. Then $1.2x=96$, so $x=\dfrac{96}{1.2}=\$80$.
QUESTION 5 [4 marks]
Hard
A store marks up an item's cost by 40\% to set the retail price, then offers a 25\% discount off the retail price during a sale. What is the sale price as a percentage of the original cost?
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Retail price $=1.40\times\text{cost}$. Sale price $=0.75\times\text{retail}=0.75\times1.40\times\text{cost}=1.05\times\text{cost}$. So the sale price is 105\% of the original cost (a net 5\% increase over cost, even after the discount).
QUESTION 6 [5 marks]
Hard
A price is increased by 25\% and then decreased by 20\%. What is the overall percent change from the original price?
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Applying both changes as multipliers: $1.25\times0.80=1.00$ — exactly the original price. So there is a $0\%$ overall change (no change), even though the two percentages don't cancel by simple subtraction ($25\%-20\%=5\%$, which is NOT the answer — percent changes compose by multiplying, not subtracting).
QUESTION 7 [5 marks]
Hard
In a school of 900 students, 60\% are enrolled in Math. Of the students enrolled in Math, 25\% are also enrolled in Physics. How many students are enrolled in both Math and Physics?
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Students enrolled in Math: $900\times0.60=540$. Of those, the number also enrolled in Physics: $540\times0.25=135$.