HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

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Example Questions

Example Question #73 : Percentages

\(\displaystyle A\) is one-third of \(\displaystyle B\), which is four-fifths of \(\displaystyle C\). What percent of \(\displaystyle A\) is \(\displaystyle C\) ?

Possible Answers:

\(\displaystyle 41 \frac{2}{3} \%\)

\(\displaystyle 26 \frac{2}{3} \%\)

\(\displaystyle 375 \%\)

\(\displaystyle 240 \%\)

Correct answer:

\(\displaystyle 375 \%\)

Explanation:

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

\(\displaystyle A\) is one-third of \(\displaystyle B\), so 

\(\displaystyle A = \frac{1}{3} B =\frac{1}{3} \cdot \frac{4}{5}C = \frac{4}{15}C\)

\(\displaystyle \frac{15} {4}\cdot A = \frac{15} {4}\cdot \frac{4}{15}C\)

\(\displaystyle \frac{15} {4} A = C\)

\(\displaystyle C\) is \(\displaystyle \frac{15} {4}\) of \(\displaystyle A\); the percent equivalent is that \(\displaystyle C\) is

\(\displaystyle \frac{15} {4} \times 100 \% = 375 \%\)

of \(\displaystyle A\)

Example Question #74 : Percentages

\(\displaystyle A\) is three-fourths of \(\displaystyle B\) and three-fifths of \(\displaystyle C\). What percent of \(\displaystyle C\) is \(\displaystyle B\) ?

Possible Answers:

\(\displaystyle 80 \%\)

\(\displaystyle 36 \%\)

\(\displaystyle 125 \%\)

\(\displaystyle 277 \frac{7}{9} \%\)

Correct answer:

\(\displaystyle 80 \%\)

Explanation:

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

\(\displaystyle A\) is three-fourths of \(\displaystyle B\) - that is, 

\(\displaystyle A = \frac{3}{4} B = \frac{3}{4} \cdot 100 = 75\).

Since \(\displaystyle A\) is also three-fifths of \(\displaystyle C\),

\(\displaystyle A = \frac{3}{5} C\)

\(\displaystyle 75 = \frac{3}{5} C\)

\(\displaystyle \frac{5} {3}\cdot 75 = \frac{5} {3}\cdot \frac{3}{5} C\)

\(\displaystyle 125 = C\)

To find what percent \(\displaystyle B\) is of \(\displaystyle C\), calculate:

\(\displaystyle \frac{B}{C} \cdot 100 \% = \frac{100}{125} \cdot 100 \% = 80 \%\)

Example Question #71 : Percentages

What is \(\displaystyle \frac{1}{3}\) % of 60?

Possible Answers:

\(\displaystyle 2,000\)

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

\(\displaystyle 1 \frac{4}{5}\)

\(\displaystyle 18,000\)

Correct answer:

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

Explanation:

 \(\displaystyle \frac{1}{3}\) % of 60 can be calculated as follows:

\(\displaystyle \frac{\frac{1}{3}}{100} \cdot 60 = \frac{1}{3} \cdot \frac{1}{100} \cdot \frac{60 }{1}= \frac{60}{300}= \frac{1}{5}\)

Example Question #76 : Percentages

\(\displaystyle \frac{2}{3}\) is what percent of \(\displaystyle \frac{5}{7}\) ?

Round to the nearest whole percent.

Possible Answers:

\(\displaystyle 210 \%\)

\(\displaystyle 47 \%\)

\(\displaystyle 93 \%\)

\(\displaystyle 107 \%\)

Correct answer:

\(\displaystyle 93 \%\)

Explanation:

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

\(\displaystyle \frac{\frac{2}{3}}{\frac{5}{7}} \times 100\)

\(\displaystyle = \frac{2}{3} \div \frac{5}{7} \times \frac{100}{1}\)

\(\displaystyle = \frac{2}{3} \times \frac{7} {5}\times \frac{100}{1}\)

\(\displaystyle =\frac{1400}{15}\)

\(\displaystyle \approx 93\)

The closest answer is 93%.

Example Question #72 : Percentages

30% of \(\displaystyle N\) is equal to 40% of what number?

Possible Answers:

\(\displaystyle \frac{4}{3}N\)

\(\displaystyle \frac{1}{12}N\)

\(\displaystyle \frac{3}{4}N\)

\(\displaystyle 12 N\)

Correct answer:

\(\displaystyle \frac{3}{4}N\)

Explanation:

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

 

\(\displaystyle \frac{3}{10}N \div \frac{4}{10} = \frac{3}{10}N \cdot \frac{10} {4} = \frac{3}{4}N\)

Example Question #73 : Percentages

\(\displaystyle N\) percent of 1,000 is equal to what percent of 5,000?

Possible Answers:

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

\(\displaystyle 20N\)

\(\displaystyle \frac{1}{20}N\)

\(\displaystyle 5N\)

Correct answer:

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

Explanation:

\(\displaystyle N\) percent of 1,000 is equal to 

\(\displaystyle \frac{N}{100} \cdot 1,000 = 10 N\)

This is

\(\displaystyle \frac{10N}{5,000} \cdot 100 = \frac{1,000N}{5,000} = \frac{1}{5}N\)

Example Question #74 : Percentages

0.5 is what percent of 0.001 ?

Possible Answers:

\(\displaystyle 5 00 \%\)

\(\displaystyle 0.2 \%\)

\(\displaystyle 0.002 \%\)

\(\displaystyle 50,000 \%\)

Correct answer:

\(\displaystyle 50,000 \%\)

Explanation:

To find what percent 0.5 is of 0.001, evaluate: 

\(\displaystyle \frac{0.5}{0.001} \times 100 \%\)

\(\displaystyle = \frac{0.5 \times 100}{0.001} \%\)

\(\displaystyle = \frac{50}{0.001} \%\)

\(\displaystyle = 50,000 \%\)

Example Question #604 : Concepts

\(\displaystyle A\) is 30% of \(\displaystyle C\)\(\displaystyle B\) is 42% of \(\displaystyle C\).

\(\displaystyle B\) is what percent of \(\displaystyle A\) ?

Possible Answers:

\(\displaystyle 40 \%\)

\(\displaystyle 140 \%\)

\(\displaystyle 28 \frac{4}{7} \%\)

\(\displaystyle 71 \frac{3}{7} \%\)

Correct answer:

\(\displaystyle 140 \%\)

Explanation:

We can choose a specific value for \(\displaystyle C\); the reasoning is independent of this value. 

Assume \(\displaystyle C = 100\). Then

\(\displaystyle A = 100 \cdot 30 \% = 100 \cdot \frac{30}{100} = 30\)

and 

\(\displaystyle B = 100 \cdot 42 \% = 100 \cdot \frac{42}{100} = 42\)

To find out what percent \(\displaystyle B\) is of \(\displaystyle A\), calculate:

\(\displaystyle \frac{B}{A} \times 100 \% = \frac{42}{30} \times 100 \% = 140 \%\)

Example Question #605 : Arithmetic

\(\displaystyle A\) is 40% of \(\displaystyle B\), which is 60% of \(\displaystyle C\). What percent of \(\displaystyle A\) is \(\displaystyle C\) ?

Possible Answers:

\(\displaystyle 416 \frac{2}{3} \%\)

\(\displaystyle 66\frac{2}{3} \%\)

\(\displaystyle 24 \%\)

\(\displaystyle 150 \%\)

Correct answer:

\(\displaystyle 416 \frac{2}{3} \%\)

Explanation:

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

\(\displaystyle B\) is 60% of \(\displaystyle C = 100\), which is 60. \(\displaystyle A\) is 40% of this, or 

\(\displaystyle A = 60 \times 40 \% = 60 \times \frac{40 }{100} = 24\).

To determine what percent \(\displaystyle C\) is of \(\displaystyle A\), calculate:

\(\displaystyle \frac{C}{A} \cdot 100 \% = \frac{100}{24} \cdot 100 \% = 416 \frac{2}{3} \%\)

 

Example Question #606 : Arithmetic

\(\displaystyle A\) is four-fifths of \(\displaystyle B\), which is three-fifths of \(\displaystyle C\). By what percent must \(\displaystyle A\) be increased to get \(\displaystyle C\) ?

Possible Answers:

\(\displaystyle 148 \%\)

\(\displaystyle 208 \frac{1}{3} \%\)

\(\displaystyle 108 \frac{1}{3} \%\)

\(\displaystyle 48 \%\)

Correct answer:

\(\displaystyle 108 \frac{1}{3} \%\)

Explanation:

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

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

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

To find out by what percent \(\displaystyle A\) must be increased to yield \(\displaystyle C\), we calculate:

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

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