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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

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6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #595 : Arithmetic

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

Possible Answers:

$240 \%$

$375 \%$

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

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

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 #1191 : Hspt Mathematics

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

Possible Answers:

$1 \frac{4}{5}$

18,000

$\frac{1}{5}$

2,000

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 #1192 : Hspt Mathematics

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

Round to the nearest whole percent.

Possible Answers:

$47 \%$

$93 \%$

$107 \%$

$210 \%$

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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Example Question #601 : Concepts

30% of is equal to 40% of what number?

Possible Answers:

$\frac{4}{3}N$

$\frac{3}{4}N$

12 N

$\frac{1}{12}N$

Correct answer:

$\frac{3}{4}N$

Explanation:

30% of is equal to $\frac{30}{100} N = \frac{3}{10}N$ . Divide by 40%, or $\frac{40}{100} = \frac{4}{10}$ , to get

$\frac{3}{10}N \div \frac{4}{10} = \frac{3}{10}N \cdot \frac{10} {4} = \frac{3}{4}N$

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Example Question #602 : Concepts

percent of 1,000 is equal to what percent of 5,000?

Possible Answers:

$\frac{1}{20}N$

$\frac{1}{5}N$

20N

Correct answer:

$\frac{1}{5}N$

Explanation:

percent of 1,000 is equal to

$\frac{N}{100} \cdot 1,000 = 10 N$

This is

$\frac{10N}{5,000} \cdot 100 = \frac{1,000N}{5,000} = \frac{1}{5}N$

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Example Question #603 : Concepts

0.5 is what percent of 0.001 ?

Possible Answers:

$5 00 \%$

$50,000 \%$

$0.002 \%$

$0.2 \%$

Correct answer:

$50,000 \%$

Explanation:

To find what percent 0.5 is of 0.001, evaluate:

$\frac{0.5}{0.001} \times 100 \%$

$= \frac{0.5 \times 100}{0.001} \%$

$= \frac{50}{0.001} \%$

$= 50,000 \%$

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

is 30% of ; is 42% of .

is what percent of ?

Possible Answers:

$28 \frac{4}{7} \%$

$140 \%$

$40 \%$

$71 \frac{3}{7} \%$

Correct answer:

$140 \%$

Explanation:

We can choose a specific value for ; the reasoning is independent of this value.

Assume C = 100 . Then

$A = 100 \cdot 30 \% = 100 \cdot \frac{30}{100} = 30$

and

$B = 100 \cdot 42 \% = 100 \cdot \frac{42}{100} = 42$

To find out what percent is of , calculate:

$\frac{B}{A} \times 100 \% = \frac{42}{30} \times 100 \% = 140 \%$

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Example Question #604 : Concepts

is 40% of , which is 60% of . What percent of is ?

Possible Answers:

$150 \%$

$24 \%$

$416 \frac{2}{3} \%$

$66\frac{2}{3} \%$

Correct answer:

$416 \frac{2}{3} \%$

Explanation:

This reasoning is independent of the value of , so choose C = 100 for simplicity's sake.

is 60% of C = 100 , which is 60. is 40% of this, or

$A = 60 \times 40 \% = 60 \times \frac{40 }{100} = 24$ .

To determine what percent is of , calculate:

$\frac{C}{A} \cdot 100 \% = \frac{100}{24} \cdot 100 \% = 416 \frac{2}{3} \%$

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Example Question #1195 : Hspt Mathematics

is four-fifths of , which is three-fifths of . By what percent must be increased to get ?

Possible Answers:

$48 \%$

$208 \frac{1}{3} \%$

$108 \frac{1}{3} \%$

$148 \%$

Correct answer:

$108 \frac{1}{3} \%$

Explanation:

This reasoning is independent of the value of , so, for simplicity's sake, we will set C = 100 .

is three-fifths of , so $B = \frac{3}{5}C = \frac{3}{5} \cdot 100 = 60$ .

is four-fifths of , so $A= \frac{4}{5}B = \frac{4}{5} \cdot 60 = 48$ .

To find out by what percent must be increased to yield , we calculate:

$\frac{C-A }{A} \times 100 \% = \frac{100-48 }{48} \times 100 \% = \frac{52}{48} \times 100 \% = 108 \frac{1}{3} \%$

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #595 : Arithmetic

Example Question #74 : Percentages

Example Question #1191 : Hspt Mathematics

Example Question #1192 : Hspt Mathematics

Example Question #601 : Concepts

Example Question #602 : Concepts

Example Question #603 : Concepts

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

Example Question #604 : Concepts

Example Question #1195 : Hspt Mathematics

All HSPT Math Resources

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