HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

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Example Questions

Example Question #1 : How To Find Percentage

Write 132% as a fraction in simplest form.

Possible Answers:

\(\displaystyle \frac{27}{20}\)

\(\displaystyle \frac{31}{25}\)

\(\displaystyle \frac{23}{20}\)

\(\displaystyle \frac{37}{25}\)

\(\displaystyle \frac{33}{25}\)

Correct answer:

\(\displaystyle \frac{33}{25}\)

Explanation:

Write as a fraction over 100, and simplify:

\(\displaystyle \frac{132}{100} = \frac{132\div 4}{100\div 4} = \frac{33}{25}\)

Example Question #2 : How To Find Percentage

Write \(\displaystyle \frac{24}{25}\) as a percent.

Possible Answers:

\(\displaystyle 96\) %

\(\displaystyle 84\) %

\(\displaystyle 98\) %

\(\displaystyle 72\) %

\(\displaystyle 88\) %

Correct answer:

\(\displaystyle 96\) %

Explanation:

Multiply by 100, and simplify:

\(\displaystyle \frac{24}{25} \times 100 = \frac{24}{25} \times \frac{100}{1} = \frac{24}{1} \times \frac{4}{1} =\frac{ 96}{1}=96\)

The correct choice is 96%.

Example Question #3 : How To Find Percentage

What percentage of \(\displaystyle 50\) is \(\displaystyle 2\)?

Possible Answers:

\(\displaystyle 500\%\)

\(\displaystyle 25\%\)

\(\displaystyle 30\%\)

\(\displaystyle 4\%\)

\(\displaystyle 20\%\)

Correct answer:

\(\displaystyle 4\%\)

Explanation:

To find the percentage, first write the values as a fraction, then convert the fraction's denominator to \(\displaystyle 100\). We can write the given values as \(\displaystyle \frac{2}{50}\), which can be converted to \(\displaystyle \frac{4}{100}\) by multiplying both the numerator and denominator by \(\displaystyle 2\)\(\displaystyle \frac{4}{100}\) is equivalent to \(\displaystyle 4\%\).

Example Question #1151 : Hspt Mathematics

What is 250% of 750?

Possible Answers:

\(\displaystyle 2,125\)

\(\displaystyle 1,750\)

\(\displaystyle 2,250\)

\(\displaystyle 2,000\)

\(\displaystyle 1,875\)

Correct answer:

\(\displaystyle 1,875\)

Explanation:

Taking 250% of a number is the same as multiplying that number by 2.5. We therefore take the product:

\(\displaystyle 750 \cdot 2.5 = 1,875\)

Example Question #1152 : Hspt Mathematics

What is 30% of 150?

Possible Answers:

\(\displaystyle 165\)

\(\displaystyle 15\)

\(\displaystyle 60\)

\(\displaystyle 50\)

\(\displaystyle 45\)

Correct answer:

\(\displaystyle 45\)

Explanation:

One way to go about solving this problem is to convert the percent into a decimal and multiply your whole number by that in order to get your answer. When converting a percent into a decimal, move the decimal point two spaces to the left:

30% = 0.30

Then, multiply this number times 150:

\(\displaystyle 150 \times 0.30 = 45\)

Your answer is \(\displaystyle 45\).

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

If \(\displaystyle 60\) is \(\displaystyle 30\%\) of \(\displaystyle x\), what is \(\displaystyle 40\%\) of \(\displaystyle x\)?

Possible Answers:

\(\displaystyle 400\)

\(\displaystyle 180\)

\(\displaystyle 1800\)

\(\displaystyle 80\)

\(\displaystyle 50\)

Correct answer:

\(\displaystyle 80\)

Explanation:

We can solve for \(\displaystyle x\) with the algebraic equation:

\(\displaystyle 0.3\cdot x=60\)

\(\displaystyle x=\frac{60}{0.3}\)

\(\displaystyle x=200\)

We can then calculate \(\displaystyle 40\%\) of \(\displaystyle x\):

\(\displaystyle 0.4\cdot200=80\)

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

What is \(\displaystyle 40\%\) of \(\displaystyle 80\)?

Possible Answers:

\(\displaystyle 40\)

\(\displaystyle 200\)

\(\displaystyle 24\)

\(\displaystyle 320\)

\(\displaystyle 32\)

Correct answer:

\(\displaystyle 32\)

Explanation:

We can convert \(\displaystyle 40\%\) to \(\displaystyle \frac{40}{100}\) or \(\displaystyle 0.4\). We can then calculate \(\displaystyle 0.4\cdot 80=32\).

Example Question #4 : How To Find The Part From The Whole With Percentage

What is \(\displaystyle 22 \frac{1}{2} \%\) of \(\displaystyle 22 \frac{1}{2}\) ?

Possible Answers:

\(\displaystyle 50\frac{5}{8}\)

\(\displaystyle 5 \frac{1}{16}\)

\(\displaystyle 100\)

\(\displaystyle 1\)

\(\displaystyle \frac{81}{160}\)

Correct answer:

\(\displaystyle 5 \frac{1}{16}\)

Explanation:

\(\displaystyle 22 \frac{1}{2} \%\) of \(\displaystyle 22 \frac{1}{2}\)  can be rewritten as 

\(\displaystyle \frac{22 \frac{1}{2} }{100} \times 22 \frac{1}{2}\)

\(\displaystyle = \frac{45}{2} \times \frac{1}{100} \times \frac{45}{2}\)

\(\displaystyle = \frac{45 \times 1 \times 45}{2 \times 100 \times 2}\)

\(\displaystyle = \frac{2,025}{400} = \frac{2,025 \div 25}{400\div 25} = \frac{81}{16} = 5 \frac{1}{16}\)

Example Question #2001 : Ssat Middle Level Quantitative (Math)

What is \(\displaystyle 8\frac{1}{3} \%\) of \(\displaystyle 666 \frac{2}{3}\) ?

Possible Answers:

\(\displaystyle 800\)

\(\displaystyle 55\frac{5}{9}\)

\(\displaystyle 80\)

\(\displaystyle 5\frac{5}{9}\)

\(\displaystyle 8,000\)

Correct answer:

\(\displaystyle 55\frac{5}{9}\)

Explanation:

 \(\displaystyle 8\frac{1}{3} \%\) of \(\displaystyle 666 \frac{2}{3} \%\) is equal to:

\(\displaystyle \frac{8 \frac{1}{3} }{100} \times 666 \frac{2}{3} \%\)

\(\displaystyle = \frac{ \frac{25}{3} }{100} \times \frac{2,000}{3}\)

\(\displaystyle = \frac{25}{3} \times \frac{1 }{100} \times \frac{2,000}{3}\)

Cross-cancel:

\(\displaystyle \frac{25}{3} \times \frac{1 }{1} \times \frac{20}{3}\)

\(\displaystyle = \frac{500}{9} = 55\frac{5}{9}\)

Example Question #1153 : Hspt Mathematics

What is 8,000% of 9,000?

Possible Answers:

\(\displaystyle 720,000\)

\(\displaystyle 888\frac{8}{9}\)

\(\displaystyle 7,200\)

\(\displaystyle 72,000,000\)

\(\displaystyle 8,888\frac{8}{9}\)

Correct answer:

\(\displaystyle 720,000\)

Explanation:

Taking 8,000%, as a decimal, is equivalent to multiplying it by \(\displaystyle 8,000 \div 100 = 80\), so 8,000% of 9,000 is equivalent to 

\(\displaystyle 80 \times 9,000 = 720,000\).

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