SSAT Upper Level

Percent Calculations

Calculating percentages, percent increase/decrease, and applied percent problems (tax, tip, discount, successive percent changes)

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Imagine downloading a massive new video game, and your screen says '40% complete.' Or maybe you are staring at a giant pepperoni pizza and decide to eat 50% of it! Percents are everywhere in the real world, and they are super fun to work with once you know their hidden secret. 🍕🎮

The word 'percent' literally means 'per 100' or 'out of 100.' So, when you see 40%, it is really just a fancy way of saying the fraction $\frac{40}{100}$ . If you have 100 pieces of chocolate candy, 40% means you get to eat 40 pieces. Yum! 🍬

On the SSAT, you will get to be a percent detective! You might need to find the percent of a specific number, or you might need to figure out the total amount if you only know a small piece of it. Think of every percent problem like a jigsaw puzzle with exactly three pieces: the Part, the Percent, and the Whole. If you know two of those pieces, you can always find the third missing piece! 🕵️‍♂️

Don't worry if it sounds a little tricky right now. Once you learn the secret code—which is just translating regular English words into math symbols—these questions become super easy and fast. For example, the word 'is' becomes an equals sign, and the word 'of' becomes a multiplication sign. Get ready to crack the code, solve the puzzles, and score big on your test!

Key Formula

Part = \frac{Percent}{100} \cdot Whole

Practice Questions

4 practice questions for SSAT Upper Level

Q1 Hard

A clothing store reduces the price of a jacket by 25%. A few weeks later, the store reduces the new price by an additional 20%. The final price of the jacket is what percent of the original price?

A 45%

B 55%

C 60%

D 65%

E 80%

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To solve successive percentage problems, it is helpful to pick a starting number, such as 100. Let the original price of the jacket be $100.

A 25% reduction means the price decreases by $25, making the new price $75.
The second reduction is 20% applied to the new price of $75.
Calculate 20% of 75: $0.20 \times 75 = 15$ .
Subtract this second discount from $75: $75 - 15 = 60$ .
The final price is $60. Since the original price was $100, the final price is exactly 60% of the original price.

Answer: C

Q2 Hard

If 75 percent of

y

is 18, what is 50 percent of

2 y

A 6

B 12

C 18

D 24

E 36

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First, translate the given information into an equation: $0.75 y = 18$ .

To find $y$ , divide both sides by 0.75 (which is the same as multiplying by $\frac{4}{3}$ ):
$y = 18 \times \frac{4}{3} = 24$ .
The question asks for 50 percent of $2 y$ .
First, calculate $2 y$ : $2 \times 24 = 48$ .
Next, find 50 percent (or half) of 48: $0.50 \times 48 = 24$ .
Alternatively, you can simplify the expression algebraically: 50% of $2 y$ is $0.50 \times 2 y = 1 y$ . Since $y = 24$ , the answer is simply 24.

Answer: D

Q3 Hard

Store A sells a particular model of bicycle for $600 and offers a 25% discount. Store B sells the exact same bicycle for $500 and offers a 15% discount. What is the positive difference between the final discounted prices at the two stores?

A $0

B $15

C $25

D $50

E $75

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First, calculate the final price at Store A.

The discount is 25% of $600: $0.25 \times 600 = 150$ .
The discounted price at Store A is $600 - 150 = 450$ .
Next, calculate the final price at Store B.
The discount is 15% of $500: $0.15 \times 500 = 75$ .
The discounted price at Store B is $500 - 75 = 425$ .
Finally, find the positive difference between the two final prices: $450 - 425 = 25$ .

Answer: C

Q4 Hard

At a certain high school, 60% of the students are girls. If 30% of the girls and 20% of the boys are on a varsity sports team, what percent of the total student body is on a varsity sports team?

A 24%

B 25%

C 26%

D 28%

E 50%

Show Solution

Let the total number of students in the high school be 100.

Since 60% of the students are girls, there are 60 girls.
The remaining students are boys, so there are $100 - 60 = 40$ boys.
Calculate the number of girls on a varsity team: 30% of 60 girls = $0.30 \times 60 = 18$ girls.
Calculate the number of boys on a varsity team: 20% of 40 boys = $0.20 \times 40 = 8$ boys.
The total number of students on a varsity team is $18 + 8 = 26$ .
Since there are 26 students on a team out of a total of 100 students, 26% of the student body is on a varsity sports team.

Answer: C

Tips & Strategies

Translate words to math symbols! On the SSAT, 'is' means $=$ , 'of' means multiply, and 'percent' means $\frac{number}{100}$ . This turns a confusing word problem into an easy equation! 📝
Look for shortcuts! If you know 20% of a number, you don't need to find the whole number to find 40%. Just multiply by 2! ⚡
Always double-check what the question is asking. Sometimes they want the 'part', sometimes the 'whole', and sometimes the leftover part (like green apples instead of red).

Common Mistakes

Watch out for answering too quickly! If a question asks for the remaining amount (like the green apples in our example), don't just stop when you find the total. Always read the last sentence twice! 🛑
Don't forget to put the numbers in the right spots! In the formula $Part = \frac{Percent}{100} \cdot Whole$ , make sure you don't mix up the 'part' and the 'whole'.

Frequently Asked Questions

What does the word 'percent' actually mean?

'Percent' comes from Latin and means 'for every 100.' So 50% just means 50 out of 100, which is exactly the same as the fraction $\frac{50}{100}$ or $\frac{1}{2}$ ! 💯

Should I use fractions or decimals for percents on the SSAT?

It depends on the problem! If the numbers are easy to simplify, like 25% becoming $\frac{1}{4}$ , fractions are usually faster. If the question already uses decimals, stick with decimals.

Are percent questions common on the SSAT?

Yes, they are! You will definitely see a few percent questions on the quantitative (math) sections. Mastering them is a great way to boost your score! 🌟

How do I quickly find 10% of any number?

Just move the decimal point one spot to the left! For example, 10% of 45 is 4.5. It's a fantastic mental math trick for the test!

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