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HSPT Math : Concepts

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Example Questions

Example Question #55 : Percentages

What percentage of is ?

Possible Answers:

$120\%$

$14\%$

$12\%$

$80\%$

$220\%$

Correct answer:

$120\%$

Explanation:

Rewrite the question in parts. A percentage is something out of $100\textup{ parts}$ .

$(\frac{x}{100})(10) = 12$

Solve for .

$(\frac{x}{10})= 12$

$x=120\%$

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

128 is $40\%$ of what number?

Possible Answers:

$51 \frac{1}{5}$

$31\frac{1}{4}$

360

300

320

Correct answer:

320

Explanation:

128 is $40\%$ of a number we will call ; alternatively, 0.40 multiplied by is equal to 128 . Set up this equation and solve for :

0.4 N = 128

$0.4 N \div 0.4 = 128\div 0.4$

N= 320

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Example Question #3 : How To Find Percentage

is what percent of 300 ?

Possible Answers:

$33 \frac{1}{3} \%$

$38 \frac{1}{2} \%$

$25 \frac{2}{3} \%$

$37 \%$

$33 \%$

Correct answer:

$25 \frac{2}{3} \%$

Explanation:

Set up the proportion statement, where is our answer, and solve:

$\frac{p}{100} = \frac{77}{300}$

$\frac{p}{100} \cdot 100 = \frac{77}{300} \cdot 100$

$p = \frac{77\cdot 100}{300} = \frac{77}{3} = 25 \frac{2}{3} \%$

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Example Question #581 : Concepts

What is $60\%$ of ?

Possible Answers:

Correct answer:

Explanation:

One way to figure out what number is a percentage of a larger number is to convert the percent into a decimal and multiply it by the whole number. Since $60\%$ is equal to 0.60 , multiply this by .

$90 \times 0.60=54$

is your answer.

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

$64\%$ of what number is 8,000 ?

Possible Answers:

15,000

16,000

14,400

12,800

12,500

Correct answer:

12,500

Explanation:

Taking 64% of a number is the same as multiplying that number by 0.64 . We can find our number, therefore, by dividing 8,000 by 0.64 :

$8,000 \div 0.64 = 12,500$

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Example Question #13 : Percentage

What is $125\%$ of 125 ?

Possible Answers:

132.5

150

100

156.25

137.5

Correct answer:

156.25

Explanation:

Rewrite $125\%$ as a decimal by writing 125 with a decimal point, then shifting it two spaces left:

$125.0\% = 1.25$

Multiply this by 125 :

$125 \times 1.25 = 156.25$

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Example Question #581 : Concepts

Convert $23.2\%$ into a decimal.

Possible Answers:

232

23.2

0.232

0.0232

2.32

Correct answer:

0.232

Explanation:

In order to convert from a percentage to a decimal, simply remove the percentage and move the decimal place back two spaces or divide by 100.

$23.2\% = \frac{232}{100}= 0.232$

The decimal conversion is: 0.232

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Example Question #164 : Grade 7

What number increased by 25% is equal to 7?

Possible Answers:

$5 \frac{3}{5}$

$5\frac{1}{4}$

$5\frac{5}{6}$

$4\frac{2}{3}$

Correct answer:

$5 \frac{3}{5}$

Explanation:

To increase a number by 25% is to take

$(100 + 25) \% = 125 \%$ of the number, or, equivalently, multiply it by

$\frac{125}{100} = \frac{125 \div 25 }{100 \div 25 } = \frac{5}{4}$ .

Therefore, we divide 7 by $\frac{5}{4}$ :

$7 \div \frac{5}{4} = \frac{7 }{1}\div \frac{5}{4} = \frac{7 }{1}\times \frac{4} {5}= \frac{7\times 4 }{1\times 5} = \frac{28}{5}$

$28 \div 5 = 5 \textup{ R }3$ , so

$\frac{28}{5} = 5 \frac{3}{5}$ .

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Example Question #165 : Grade 7

What number decreased by 25% is equal to 7?

Possible Answers:

$8\frac{3}{4}$

$8\frac{2}{5}$

$9 \frac{1}{7}$

$9 \frac{1}{3}$

Correct answer:

$9 \frac{1}{3}$

Explanation:

To decrease a number by 25% is to take

$(100 - 25) \% = 75 \%$ of the number, or, equivalently, multiply it by

$\frac{75}{100} = \frac{75 \div 25 }{100 \div 25 } = \frac{3}{4}$ .

Therefore, we divide 7 by $\frac{3}{4}$ :

$7 \div \frac{3}{4} = \frac{7 }{1}\div \frac{3}{4} = \frac{7 }{1}\times \frac{4} {3}= \frac{7\times 4 }{1\times 3} = \frac{28}{3}$

$28 \div 3 = 9 \textup{ R }1$ , so

$\frac{28}{3} = 9 \frac{1}{3}$ .

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Example Question #1184 : Hspt Mathematics

What is $3 \frac{1}{2}$ increased by 30%?

Possible Answers:

$3 \frac{4}{5}$

$3 \frac{13}{2 0}$

$4 \frac{1}{5}$

$4 \frac{11}{2 0}$

Correct answer:

$4 \frac{11}{2 0}$

Explanation:

Increasing a number by 30% is equivalent to taking 130% of a number, which in turn is equivalent to multiplying it by

$\frac{130}{100} = \frac{130 \div 10}{100 \div 10} = \frac{13}{10}$ .

$3 \frac{1}{2}$ increased by 30% is the product of $3 \frac{1}{2}$ and $\frac{13}{10}$ :

$3 \frac{1}{2} \times \frac{13}{10}$

$= \frac{3 \times 2 + 1}{2} \times \frac{13}{10}$

$= \frac{7}{2} \times \frac{13}{10}$

$= \frac{7 \times 13}{2 \times 10}$

$= \frac{91}{2 0}$

$91 \div 20 = 4 \textup{ R }11$ , so this quantity is equal to $4 \frac{11}{2 0}$ , the correct answer.

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #55 : Percentages

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

Example Question #3 : How To Find Percentage

Example Question #581 : Concepts

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

Example Question #13 : Percentage

Example Question #581 : Concepts

Example Question #164 : Grade 7

Example Question #165 : Grade 7

Example Question #1184 : Hspt Mathematics

All HSPT Math Resources

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