HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

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Example Questions

Example Question #581 : Concepts

Convert \displaystyle 23.2\% into a decimal.

Possible Answers:

\displaystyle 232

\displaystyle 23.2

\displaystyle 0.232

\displaystyle 0.0232

\displaystyle 2.32

Correct answer:

\displaystyle 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.

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

The decimal conversion is:  \displaystyle 0.232

Example Question #164 : Grade 7

What number increased by 25% is equal to 7?

Possible Answers:

\displaystyle 5 \frac{3}{5}

\displaystyle 5\frac{1}{4}

\displaystyle 5\frac{5}{6}

\displaystyle 4\frac{2}{3}

Correct answer:

\displaystyle 5 \frac{3}{5}

Explanation:

To increase a number by 25% is to take

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

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

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

\displaystyle 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}

, so

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

Example Question #165 : Grade 7

What number decreased by 25% is equal to 7?

Possible Answers:

\displaystyle 8\frac{3}{4}

\displaystyle 8\frac{2}{5}

\displaystyle 9 \frac{1}{7}

\displaystyle 9 \frac{1}{3}

Correct answer:

\displaystyle 9 \frac{1}{3}

Explanation:

To decrease a number by 25% is to take

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

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

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

\displaystyle 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}

, so

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

Example Question #1184 : Hspt Mathematics

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

Possible Answers:

\displaystyle 3 \frac{4}{5}

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

\displaystyle 4 \frac{1}{5}

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

Correct answer:

\displaystyle 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 

\displaystyle \frac{130}{100} = \frac{130 \div 10}{100 \div 10} = \frac{13}{10}

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

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

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

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

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

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

, so this quantity is equal to \displaystyle 4 \frac{11}{2 0}, the correct answer.

Example Question #591 : Arithmetic

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

Possible Answers:

\displaystyle 1 \frac{4}{5}

\displaystyle 2 \frac{1 }{3}

\displaystyle 2 \frac{1 }{10}

\displaystyle 3 \frac{3}{10}

Correct answer:

\displaystyle 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 

\displaystyle \frac{60}{100} = \frac{60 \div 20}{100 \div 20} = \frac{3}{5}

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

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

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

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

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

\displaystyle = \frac{21 }{10}

, so the correct response is \displaystyle 2 \frac{1 }{10}.

Example Question #1181 : Hspt Mathematics

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

Select the closest answer.

Possible Answers:

\displaystyle 20 \%

\displaystyle 15 \%

\displaystyle 25 \%

\displaystyle 30 \%

Correct answer:

\displaystyle 20 \%

Explanation:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

, so

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

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

Example Question #591 : Concepts

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

Select the closest answer.

Possible Answers:

\displaystyle 30 \%

\displaystyle 20 \%

\displaystyle 25 \%

\displaystyle 35 \%

Correct answer:

\displaystyle 30 \%

Explanation:

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

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

This represents an increase of 

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

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

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

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

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

, so this is \displaystyle 29 \frac{1}{6}\%.

Tthe response closest to the correct percent is 30%.

Example Question #592 : Arithmetic

\displaystyle X is 40% of 150.

\displaystyle Y is 30% of 200.

\displaystyle Z is 20% of 225.

Which are equal to each other/one another?

Possible Answers:

\displaystyle X and \displaystyle Z

\displaystyle Y and \displaystyle Z

\displaystyle X and \displaystyle Y

No two of \displaystyle X\displaystyle Y, and \displaystyle Z are equal.

Correct answer:

\displaystyle X and \displaystyle Y

Explanation:

\displaystyle X is 40% of 150, which is

\displaystyle 150 \times 0.40 = 60

\displaystyle Y is 30% of 200, which is 

\displaystyle 200 \times 0.30 = 60

\displaystyle Z is 20% of 225, which is 

\displaystyle 225 \times 0.20 = 45

The correct response is \displaystyle Z < X = Y.

Example Question #1182 : Hspt Mathematics

What is the percentage of male students in a class if \displaystyle 15 are male out of \displaystyle 20 students?

Possible Answers:

\displaystyle 60%

\displaystyle 50\%

\displaystyle 75\%

\displaystyle 100\%

Correct answer:

\displaystyle 75\%

Explanation:

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

You can reduce this fraction by \displaystyle 5 since both the numerator and denominator are divisible by it.  

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

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

So that gives you \displaystyle 75\%.

Example Question #593 : Arithmetic

\displaystyle A is 85% of \displaystyle B.

What percent \displaystyle A must be increased by to obtain \displaystyle B?

(Choose the closest answer)

Possible Answers:

\displaystyle 15 \%

\displaystyle 16 \%

\displaystyle 17 \%

\displaystyle 18 \%

Correct answer:

\displaystyle 18 \%

Explanation:

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

\displaystyle A is 85% of \displaystyle B, so \displaystyle A = 85.

To find out by what percent \displaystyle A must be increased by to obtain \displaystyle B, calculate

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

This is

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

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

 

\displaystyle \approx 17.6 \%

The correct choice is 18%.

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