HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

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Example Questions

Example Question #3 : How To Find The Whole From The Part With Percentage

32 is \displaystyle 2 \frac{1}{2} % of what number?

Possible Answers:

\displaystyle 128

\displaystyle 1,280

\displaystyle 7\frac{7}{8}

\displaystyle 800

\displaystyle \frac{4}{5}

Correct answer:

\displaystyle 1,280

Explanation:

We can rewrite \displaystyle 2 \frac{1}{2} % as 2.5%. 32 is 2.5% of a number \displaystyle N, or, equivalently, 0.025 multiplied by a number \displaystyle N is equal to 32. We can write this as an equation and solve for \displaystyle N:

\displaystyle 0.025 N = 32

\displaystyle 0.025 N \div 0.025 = 32 \div 0.025

\displaystyle N = 1,280

 

Example Question #571 : Arithmetic

3,200 is 160% of what number?

Possible Answers:

\displaystyle 5,120

\displaystyle 2,133\frac{1}{3}

\displaystyle 3,040

\displaystyle 2,400

\displaystyle 2,000

Correct answer:

\displaystyle 2,000

Explanation:

Set up the proportion statement and solve for \displaystyle N by cross-multiplying:

\displaystyle \frac{3,200}{N}= \frac{160}{100}

\displaystyle N \cdot 160 = 3,200 \cdot 100 = 320,000

\displaystyle N \cdot 160 \div 160 = 320,000\div 160

\displaystyle N = 2,000

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

12 is \displaystyle \frac{3}{4} \% of what number?

Possible Answers:

\displaystyle 900

\displaystyle \frac{9}{100}

\displaystyle 16

\displaystyle 9

\displaystyle 1,600

Correct answer:

\displaystyle 1,600

Explanation:

Set up the proportion statement and solve for \displaystyle N by cross-multiplying:

\displaystyle \frac{12}{N } = \frac{\frac{3}{4}}{100}

\displaystyle \frac{3}{4} \cdot N = 12 \cdot 100 = 1,200

\displaystyle \frac{4}{3} \cdot \frac{3}{4} \cdot N = \frac{4}{3} \cdot 1,200

\displaystyle N = \frac{4,800}{3} =1,600

Example Question #572 : Arithmetic

Convert \displaystyle 64.32\% into a decimal.

Possible Answers:

\displaystyle 6432

\displaystyle 64.32

\displaystyle 0.006432

\displaystyle 0.6432

\displaystyle 0.06432

Correct answer:

\displaystyle 0.6432

Explanation:

To covert a percent to a decimal, simply remove the percent sign and divide by 100.

\displaystyle 64.32\%= \frac{64.32}{100}=0.6432

Example Question #571 : Concepts

What percentage of \displaystyle 80 is \displaystyle 50?

Possible Answers:

\displaystyle 40\%

\displaystyle 36.5\%

\displaystyle 62.5\%

\displaystyle 30\%

\displaystyle 160\%

Correct answer:

\displaystyle 62.5\%

Explanation:

Set up an equation that represents this scenario.  The question asks what percent of a number is another number.  Keep in mind, the percent of a number is over 100.  

\displaystyle \frac{x}{100}(80)= 50 or \displaystyle \frac{x}{100}\times \frac{80}{1}=\frac{80x}{100}=50

We can reduce \displaystyle \frac{80}{100} to \displaystyle \frac{4}{5} by dividing both the numerator and the denominator by \displaystyle 20

\displaystyle \frac{4}{5}x = 50

Now we want to isolate the x by itself. First we multiply each side by \displaystyle 5

\displaystyle 4x=250

Then divide each side by \displaystyle 4.

\displaystyle x=\frac{250}{4}= \frac{125}{2}= 0.625 = 62.5\%

Check:  Does \displaystyle 62.5\% of \displaystyle 80 equal \displaystyle 50?

\displaystyle 0.625(80)=50

The correct answer is:  \displaystyle 62.5\%

Example Question #52 : Percentages

Add the percentages and find the answer in decimal:  \displaystyle 3\%+3.5\%+100\%

Possible Answers:

\displaystyle 7.5%

\displaystyle 1.065

\displaystyle 1.038

\displaystyle 0.1065

\displaystyle 10.65

Correct answer:

\displaystyle 1.065

Explanation:

Add the percentages.

\displaystyle 3\%+3.5\%+100\%= 106.5\%

To turn the answer into decimal form, simply divide by 100 or move the decimal place back two units to the left and remove the percentage sign.

The answer is:  \displaystyle 1.065

Example Question #574 : Concepts

What is \displaystyle 10\% of \displaystyle 2?

Possible Answers:

\displaystyle \frac{1}{20}

\displaystyle \frac{1}{2}

\displaystyle \frac{1}{10}

\displaystyle \frac{1}{50}

\displaystyle \frac{1}{5}

Correct answer:

\displaystyle \frac{1}{5}

Explanation:

Rewrite \displaystyle 10\% as a fraction.

\displaystyle 10\%= \frac{1}{10}

Multiply this value with two.

\displaystyle \frac{1}{10}\times 2 = \frac{1}{5}

Example Question #573 : Arithmetic

Add the percentages:  \displaystyle 6\%+20\%+86\%

Possible Answers:

\displaystyle 12

\displaystyle 1.12\%

\displaystyle 0.12

\displaystyle 112\%

\displaystyle 11.2\%

Correct answer:

\displaystyle 112\%

Explanation:

Add the ones digit.

\displaystyle 6+0+6 = 12

The ones digit is two.

Carry over the tens digit since this number is ten or greater.

Add the tens digits with the carryover.

\displaystyle 0+2+8+(1) = 11

The hundreds and the tens digit is one.

The answer is: \displaystyle 112\%

Example Question #571 : Concepts

What is \displaystyle 6\% of \displaystyle 30?

Possible Answers:

\displaystyle 5

\displaystyle 3.3

\displaystyle 24

\displaystyle 1.8

\displaystyle \frac{1}{5}

Correct answer:

\displaystyle 1.8

Explanation:

Six percent is six out of a hundred parts.

\displaystyle 6\% = \frac{6}{100}

Multiply this with 30.

\displaystyle \frac{6}{100}\times 30 = \frac{180}{100} = 1.8

Example Question #1172 : Hspt Mathematics

Possible Answers:

\displaystyle \frac{1}{7}

\displaystyle 17

\displaystyle 7

\displaystyle \frac{1}{10}

\displaystyle 10

Correct answer:

\displaystyle 7

Explanation:

Rewrite \displaystyle 10\% as a decimal or fraction.

\displaystyle 10\%=0.1 = \frac{1}{10}

Multiply either value with \displaystyle 70.

\displaystyle \frac{1}{10} (70) = 7

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