SSAT Middle 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

5 practice questions for SSAT Middle Level

Q1 Medium

A pair of shoes originally costs $60.00. They are on sale for 20% off. After the discount is applied, a 5% sales tax is added to the sale price. What is the final cost of the shoes?

A $45.60

B $48.00

C $50.40

D $51.00

E $65.00

Show Solution

First, find the amount of the discount: $0.20 \times 60 = 12$ . Subtract this from the original price to find the sale price: $60 - 12 = 48$ . Next, calculate the 5% sales tax on the sale price: $0.05 \times 48 = 2.40$ . Finally, add the tax to the sale price to find the total cost: $48.00 + 2.40 = 50.40$ .

Answer: C

Q2 Medium

What is 24% of 150?

A 24

B 30

C 36

D 42

E 48

Show Solution

To find 24% of 150, multiply 150 by the decimal equivalent of 24%, which is 0.24. $0.24 \times 150 = 36$ . Alternatively, you can find 1% of 150, which is 1.5, and multiply by 24: $24 \times 1.5 = 36$ .

Answer: C

Q3 Medium

If 15% of a number is 60, what is 40% of the number?

A 100

B 120

C 150

D 160

E 240

Show Solution

Let $x$ be the unknown number. You know that $0.15 x = 60$ . Divide both sides by 0.15 to find the number: $x = \frac{60}{0.15} = 400$ . Now, find 40% of 400 by multiplying 400 by 0.40: $0.40 \times 400 = 160$ .

Answer: D

Q4 Medium

A library had 80 books checked out on Monday. On Tuesday, 100 books were checked out. What was the percent increase in the number of books checked out from Monday to Tuesday?

A 15%

B 20%

C 25%

D 80%

E 125%

Show Solution

First, find the amount of increase by subtracting the original amount from the new amount: $100 - 80 = 20$ . Next, divide the increase by the original amount and multiply by 100 to find the percent increase: $\frac{20}{80} \times 100 = \frac{1}{4} \times 100 = 25%$ .

Answer: C

Q5 Medium

Sarah spent 30% of her monthly allowance on a new video game. If the video game cost $18, how much is her total monthly allowance?

A $36

B $48

C $54

D $60

E $72

Show Solution

Let $a$ represent Sarah's total monthly allowance. The problem states that 30% of her allowance is $18, which can be written as $0.30 a = 18$ . To find $a$ , divide both sides by 0.30: $a = \frac{18}{0.30} = 60$ . Her total allowance is $60.

Answer: D

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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