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HSPT Math : Arithmetic

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Example Questions

Example Question #591 : Concepts

What is $3 \frac{1}{2}$ decreased by 40%?

Possible Answers:

$2 \frac{1 }{10}$

$2 \frac{1 }{3}$

$1 \frac{4}{5}$

$3 \frac{3}{10}$

Correct answer:

$2 \frac{1 }{10}$

Explanation:

Decreasing a number by 40% is equivalent to taking 60% of a number, which in turn is equivalent to multiplying it by

$\frac{60}{100} = \frac{60 \div 20}{100 \div 20} = \frac{3}{5}$ .

$3 \frac{1}{2}$ decreased by 40% is the product of $3 \frac{1}{2}$ and $\frac{3}{5}$ :

$3 \frac{1}{2} \times \frac{3}{5}$

$= \frac{3 \times 2 + 1}{2} \times \frac{3}{5}$

$= \frac{7}{2} \times \frac{3}{5}$

$= \frac{7\times 3 }{2\times 5}$

$= \frac{21 }{10}$

$21 \div 10 = 2 \textup{ R }1$ , so the correct response is $2 \frac{1 }{10}$ .

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Example Question #63 : Percentages

6 decreased by what percent is $4\frac{2}{3}$ ?

Select the closest answer.

Possible Answers:

$15 \%$

$20 \%$

$25 \%$

$30 \%$

Correct answer:

$20 \%$

Explanation:

The difference of 6 and $4\frac{2}{3}$ is

$6 - 4\frac{2}{3}$

$= \frac{6 \times 3}{3} - \frac{4 \times 3+ 2}{3}$

$= \frac{18}{3} - \frac{14}{3}$

$= \frac{18-14}{3}$

$= \frac{ 4}{3}$ .

Therefore, 6 is being decreased by $\frac{ 4}{3}$ ; to find out what percent this is of 6, we calculate:

$\frac{\frac{ 4}{3}}{6} \times 100 \%$

$=\left ( \frac{ 4}{3} \div 6 \right ) \times 100 \%$

$=\left ( \frac{ 4}{3} \times \frac{1}{6} \right ) \times 100 \%$

$=\left ( \frac{ 2}{3} \times \frac{1}{3} \right ) \times \frac{100 }{1}\%$

$=\left ( \frac{ 2 \times 1 \times 100}{3 \times 3 \times 1} \right ) \%$

$= \frac{ 2 00}{9} \%$

$2 00 \div 9 = 22 \textup{ R 2}$ , so

$\frac{ 2 00}{9} \% = 22\frac{ 2 }{9} \%$ .

The answer that comes closest among the four choices is 20%.

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Example Question #64 : Percentages

12 increased by what percent is $15\frac{1}{2}$ ?

Select the closest answer.

Possible Answers:

$30 \%$

$35 \%$

$20 \%$

$25 \%$

Correct answer:

$30 \%$

Explanation:

The difference of $15\frac{1}{2}$ and 12 is

$15\frac{1}{2} - 12= 3\frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2}$ .

This represents an increase of

$\frac{\frac{7}{2}}{12} \times 100 \%$

$= \left ( \frac{7}{2} \div 12 \right ) \times 100 \%$

$= \left ( \frac{7}{2} \times \frac{1}{12 } \right ) \times \frac{100 }{1}\%$

$= \left ( \frac{7}{2} \times \frac{1}{3} \right ) \times \frac{25}{1}\%$

$= \frac{175}{6}\%$

$175 \div 6 = 29 \textup{ R }1$ , so this is $29 \frac{1}{6}\%$ .

Tthe response closest to the correct percent is 30%.

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Example Question #591 : Arithmetic

is 40% of 150.

is 30% of 200.

is 20% of 225.

Which are equal to each other/one another?

Possible Answers:

and

No two of , , and are equal.

and

Correct answer:

and

Explanation:

is 40% of 150, which is

$150 \times 0.40 = 60$

is 30% of 200, which is

$200 \times 0.30 = 60$

is 20% of 225, which is

$225 \times 0.20 = 45$

The correct response is Z < X = Y .

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Example Question #11 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

What is the percentage of male students in a class if are male out of students?

Possible Answers:

$100\%$

$50\%$

$75\%$

60%

Correct answer:

$75\%$

Explanation:

First you want to make a proportion so $\frac{15}{20}$ of the class are male.

You can reduce this fraction by since both the numerator and denominator are divisible by it.

This gives you $\frac{3}{4}$ which as a decimal is 0.75 .

To make that into a percentage, you multiple by 100 and add a "%" symbol.

So that gives you $75\%$ .

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Example Question #591 : Concepts

is 85% of .

What percent must be increased by to obtain ?

(Choose the closest answer)

Possible Answers:

$15 \%$

$17 \%$

$16 \%$

$18 \%$

Correct answer:

$18 \%$

Explanation:

The reasoning is independent of the value of , so assume that B = 100 .

is 85% of , so A = 85 .

To find out by what percent must be increased by to obtain , calculate

$\frac{B - A}{A} \cdot 100 \%$

This is

$\frac{100 - 85 }{85} \cdot 100 \%$

$\frac{1 5 }{85} \cdot 100 \%$

$\approx 17.6 \%$

The correct choice is 18%.

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Example Question #71 : Percentages

is one-third of , which is four-fifths of . What percent of is ?

Possible Answers:

$240 \%$

$375 \%$

$41 \frac{2}{3} \%$

$26 \frac{2}{3} \%$

Correct answer:

$375 \%$

Explanation:

is four-fifths of , so $B = \frac{4}{5}C$ .

is one-third of , so

$A = \frac{1}{3} B =\frac{1}{3} \cdot \frac{4}{5}C = \frac{4}{15}C$

$\frac{15} {4}\cdot A = \frac{15} {4}\cdot \frac{4}{15}C$

$\frac{15} {4} A = C$

is $\frac{15} {4}$ of ; the percent equivalent is that is

$\frac{15} {4} \times 100 \% = 375 \%$

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Example Question #74 : Percentages

is three-fourths of and three-fifths of . What percent of is ?

Possible Answers:

$277 \frac{7}{9} \%$

$125 \%$

$36 \%$

$80 \%$

Correct answer:

$80 \%$

Explanation:

For simplicity's sake, we will set B = 100 ; this reasoning is independent of the value of .

is three-fourths of - that is,

$A = \frac{3}{4} B = \frac{3}{4} \cdot 100 = 75$ .

Since is also three-fifths of ,

$A = \frac{3}{5} C$

$75 = \frac{3}{5} C$

$\frac{5} {3}\cdot 75 = \frac{5} {3}\cdot \frac{3}{5} C$

125 = C

To find what percent is of , calculate:

$\frac{B}{C} \cdot 100 \% = \frac{100}{125} \cdot 100 \% = 80 \%$

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Example Question #592 : Arithmetic

What is $\frac{1}{3}$ % of 60?

Possible Answers:

18,000

$1 \frac{4}{5}$

2,000

$\frac{1}{5}$

Correct answer:

$\frac{1}{5}$

Explanation:

$\frac{1}{3}$ % of 60 can be calculated as follows:

$\frac{\frac{1}{3}}{100} \cdot 60 = \frac{1}{3} \cdot \frac{1}{100} \cdot \frac{60 }{1}= \frac{60}{300}= \frac{1}{5}$

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Example Question #593 : Arithmetic

$\frac{2}{3}$ is what percent of $\frac{5}{7}$ ?

Round to the nearest whole percent.

Possible Answers:

$210 \%$

$93 \%$

$107 \%$

$47 \%$

Correct answer:

$93 \%$

Explanation:

To calculate what percent $\frac{2}{3}$ is of $\frac{5}{7}$ , evaluate:

$\frac{\frac{2}{3}}{\frac{5}{7}} \times 100$

$= \frac{2}{3} \div \frac{5}{7} \times \frac{100}{1}$

$= \frac{2}{3} \times \frac{7} {5}\times \frac{100}{1}$

$=\frac{1400}{15}$

$\approx 93$

The closest answer is 93%.

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HSPT Math : Arithmetic

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #591 : Concepts

Example Question #63 : Percentages

Example Question #64 : Percentages

Example Question #591 : Arithmetic

Example Question #11 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

Example Question #591 : Concepts

Example Question #71 : Percentages

Example Question #74 : Percentages

Example Question #592 : Arithmetic

Example Question #593 : Arithmetic

All HSPT Math Resources

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