HSPT Math : Percentages

Study concepts, example questions & explanations for HSPT Math

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Example Questions

Example Question #61 : Arithmetic

The price of a suit after a 20% employee discount is $240.00. What is the original price?

Possible Answers:

\(\displaystyle \$280.00\)

\(\displaystyle \$192.00\)

\(\displaystyle \$260.00\)

\(\displaystyle \$300.00\)

\(\displaystyle \$288.00\)

Correct answer:

\(\displaystyle \$300.00\)

Explanation:

Deducting a 20% discount is the same as charging 80% of the price, so $240.00 is 80% of the original price, which we call \(\displaystyle P\). Just solve this equation:

\(\displaystyle P \cdot 0.80 = 240.00\)

\(\displaystyle P = 240 \div 0.80 = 300.00\)

The suit originally cost $300.00

Example Question #62 : Problem Solving

Express  \(\displaystyle 7 \tfrac{1}{2}\) %  as a fraction in lowest terms.

Possible Answers:

\(\displaystyle \frac{6}{80}\)

\(\displaystyle \frac{150}{2,000}\)

\(\displaystyle \frac{75}{1,000}\)

\(\displaystyle \frac{3}{40}\)

\(\displaystyle \frac{15}{200}\)

Correct answer:

\(\displaystyle \frac{3}{40}\)

Explanation:

Put the percent over 100 and simplify as follows:

\(\displaystyle \frac{7 \tfrac{1}{2} }{100} = 7 \tfrac{1}{2} \div 100 = \frac{15}{2} \cdot \frac{1}{100} =\frac{3}{2} \cdot \frac{1}{20} = \frac{3}{40}\)

Note: all of these choices are equivalent to \(\displaystyle 7 \tfrac{1}{2}\) %; but only \(\displaystyle \frac{3}{40}\) is in lowest terms.

 

Example Question #3 : Percentages

A store normally sells a certain coat for $40.  For the holidays it offers a sale where the new price of the coat is now $30.  What percent discount is the store selling the coat for?

Possible Answers:

\(\displaystyle 10\%\) discount

\(\displaystyle 30\%\) discount

\(\displaystyle 5\%\) discount

\(\displaystyle 25\%\) discount

\(\displaystyle 40\%\) discount

Correct answer:

\(\displaystyle 25\%\) discount

Explanation:

The coat is $10 cheaper than normal. 

\(\displaystyle \frac{10}{40}=0.25=25\%\)

Example Question #2 : How To Work With Percentages

Marshal saves 10% of his paycheck each week. If Marshal earned $652.20 this week, approximately how much money did he save?

Possible Answers:

\(\displaystyle \$55\)

\(\displaystyle \$30\)

\(\displaystyle \$70\)

\(\displaystyle \$7\)

\(\displaystyle \$60\)

Correct answer:

\(\displaystyle \$70\)

Explanation:

The word approximately tells you that you need to estimate to get the answer. $652.20 can round up to $700 because 52.20 is more than half of 100. Since 10% is equal to the decimal 0.10, we multiply 700 by this number in order to find out what 10% of 700 is.

\(\displaystyle 700\times 0.10 = 70\)

The answer is  \(\displaystyle \$70\)

Example Question #3 : How To Work With Percentages

The sales tax rate for a particular locality is 9%. How much will be paid after tax for $154.92 worth of groceries?

Possible Answers:

\(\displaystyle \$ 169.36\)

\(\displaystyle \$ 168.86\)

\(\displaystyle \$ 169.06\)

\(\displaystyle \$ 168.16\)

\(\displaystyle \$ 167.26\)

Correct answer:

\(\displaystyle \$ 168.86\)

Explanation:

Multiply the price of the groceries before tax - $154.92 - by the decimal equivalent of 9% , which is 0.09. Round this tax to the nearest hundredth (cents), then add to the price of the groceries.

Tax: \(\displaystyle \$154.92 \cdot 0.09 \approx \$13.94\)

Price after tax: \(\displaystyle \$154.92 + \$13.94 =\$168.86\)

Example Question #3 : Percentage

Susan has a coupon for 10% off any one item at her favorite department store. There is also a storewide sale of 50% off all purchases. 

If Susan wants to by a shirt originally priced at $42, how much will she pay?

Possible Answers:

$18.90

$37.80

$21.00

$20.00

$16.50

Correct answer:

$18.90

Explanation:

The storewide sale discounts the shirt by 50%:

\(\displaystyle .5\times \$42=\$21\)

Susan also has the 10% off coupon, so she's really paying 90% of the cost of the shirt:

\(\displaystyle .9\times \$21=\$18.90\)

 

Example Question #4 : Percentages

Exactly \(\displaystyle \frac{1}{3}\) of the plants in a garden are tomato plants.  Which of the following could be the total number of plants in the garden?

Possible Answers:

\(\displaystyle 20\)

\(\displaystyle 22\)

\(\displaystyle 18\)

\(\displaystyle 16\)

\(\displaystyle 14\)

Correct answer:

\(\displaystyle 18\)

Explanation:

The total number of plants has to be divisible by 3.  Of the answer choices, the only one that is divisible by 3 is 18.  You can check this because numbers that are divisible have the sum of their digits also divisible by 3. For example,

\(\displaystyle 1 + 8 = 9\) 

which is divisible by 3, so 18 is divisible by 3.

Example Question #1 : How To Find The Whole From The Part With Percentage

To get on the ballot for student body president, a student must turn in a petition with the signatures of 3% of the students. If there are 5,319 students, how many signatures must a student get to be on that ballot? (Nearest whole person)

Possible Answers:

\(\displaystyle 1,596\)

\(\displaystyle 220\)

\(\displaystyle 1,064\)

\(\displaystyle 106\)

\(\displaystyle 160\)

Correct answer:

\(\displaystyle 160\)

Explanation:

3% of 5,319 can be calculated by multiplying 5,319 by 0.03, the decimal equivalent of 3%:

\(\displaystyle 5,319 \times 0.03 = ?\)

Multiply 5,319 by 3, then move the decimal point so that two digits are to the right:

\(\displaystyle 5,319 \times 3 =15,957\),

so

\(\displaystyle 5,319 \times 0.03 = 159.57\)

Rounded to the nearest whole number, this is 160 signatures.

Example Question #5 : Percentages

A laptop computer is on sale for 40% less than the original price. If the original price is $345.00, what is the laptop's current sale price?

 

 

Possible Answers:

\(\displaystyle 207.00\)

\(\displaystyle 138.00\)

\(\displaystyle 385.00\)

\(\displaystyle 305.00\)

Correct answer:

\(\displaystyle 207.00\)

Explanation:

First, multiply the original price by the sale percentage:

\(\displaystyle 345 *.40=138\)

Then, subtract that amount from the original price to get the sale price:

\(\displaystyle 345-138=207\).

The laptop's current sale price is \(\displaystyle \$ 207.00\)

Example Question #3 : Percentages

Helen wants to buy a dress for a party. It is on sale for 37% off. How much does the dress currently costs, if its original price was $45.00?

 

 

Possible Answers:

\(\displaystyle \$82.50\)

\(\displaystyle \$16.65\)

\(\displaystyle \$28.35\)

\(\displaystyle \$8.00\)

Correct answer:

\(\displaystyle \$28.35\)

Explanation:

First, multiply 45 by 0.37:

\(\displaystyle 45 * .37=16.65\)

Then, subtract that amount from 45.00 to find the sale price:

\(\displaystyle 45-16.65=28.35\)

Answer: The dress' sale price is $28.35.

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