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HSPT Quantitative : How to manipulate numbers

Study concepts, example questions & explanations for HSPT Quantitative

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6 Diagnostic Tests 55 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #71 : How To Manipulate Numbers

$\displaystyle 40$ percent of 2080 $\displaystyle 2080$ is what number?

Possible Answers:

832 $\displaystyle 832$

840 $\displaystyle 840$

796 $\displaystyle 796$

882 $\displaystyle 882$

Correct answer:

832 $\displaystyle 832$

Explanation:

Multiply 2080 $\displaystyle 2080$ by the decimal version of $\displaystyle 40$ percent:

$2080\cdot.40=832$ $\displaystyle 2080\cdot.40=832$

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Example Question #72 : Number Manipulation*

$\displaystyle 8$ is $\displaystyle 16$ percent of what number?

Possible Answers:

$\displaystyle 42$

$\displaystyle 56$

$\displaystyle 46$

$\displaystyle 50$

Correct answer:

$\displaystyle 50$

Explanation:

Representing the unknown number with an $\displaystyle x$, we know that 8=.16x $\displaystyle 8=.16x$. Divide both sides by $\displaystyle .16$ to solve for $\displaystyle x$:

$x=\frac{8}{.16}=50$ $\displaystyle x=\frac{8}{.16}=50$

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Example Question #72 : How To Manipulate Numbers

What is the difference between (7+2)^2 $\displaystyle (7+2)^2$ and 7^2+2^2 $\displaystyle 7^2+2^2$

Possible Answers:

$\displaystyle 0$

134 $\displaystyle 134$

$\displaystyle 53$

$\displaystyle 28$

Correct answer:

$\displaystyle 28$

Explanation:

Calculate what's in the parentheses before exponents:

$\displaystyle (7+2)^2=9^2=81$

$\displaystyle 7^2+2^2=49+4=53$

Subtract to find the difference:

$\displaystyle 81-53=28$

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Example Question #73 : How To Manipulate Numbers

What number is $\displaystyle 45$ percent of $\displaystyle 60$?

Possible Answers:

$\displaystyle 34$

$\displaystyle 22$

$\displaystyle 21$

$\displaystyle 27$

Correct answer:

$\displaystyle 27$

Explanation:

Multiply $\displaystyle 60$ by the decimal version of $\displaystyle 45$ percent:

$60\cdot.45=27$ $\displaystyle 60\cdot.45=27$

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Example Question #74 : How To Manipulate Numbers

What is $\displaystyle 5$ less than the product of $\displaystyle 13$ and $\displaystyle 6$?

Possible Answers:

$\displaystyle 83$

$\displaystyle 78$

$\displaystyle 82$

$\displaystyle 73$

Correct answer:

$\displaystyle 73$

Explanation:

First find the product:

$13\cdot6=78$ $\displaystyle 13\cdot6=78$

Then subtract $\displaystyle 5$:

78-5=73 $\displaystyle 78-5=73$

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Example Question #75 : How To Manipulate Numbers

What is the square root of the number that is $\displaystyle 9$ less than the product of $\displaystyle 6$ and $\displaystyle 15$?

Possible Answers:

$\displaystyle 9$

$\displaystyle 11$

$\displaystyle 8$

$\displaystyle 10$

Correct answer:

$\displaystyle 9$

Explanation:

First, find the product of $\displaystyle 6$ and $\displaystyle 15$:

$6\cdot15=90$ $\displaystyle 6\cdot15=90$

Next, subtract 9:

90-9=81 $\displaystyle 90-9=81$

Finally, the square root of $\displaystyle 81$ is $\displaystyle 9$, because $9\cdot9=81$ $\displaystyle 9\cdot9=81$.

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Example Question #76 : Number Manipulation*

What is $\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of $\displaystyle 30$ percent of $\displaystyle 70$?

Possible Answers:

$6 \frac{1}{3}$ $\displaystyle 6 \frac{1}{3}$

$\displaystyle 7$

$\displaystyle 12$

$4 \frac{1}{2}$ $\displaystyle 4 \frac{1}{2}$

Correct answer:

$\displaystyle 7$

Explanation:

First, find $\displaystyle 30$ percent of $\displaystyle 70$:

$70\cdot.30=21$ $\displaystyle 70\cdot.30=21$

Then, find $\frac{1}3$ $\displaystyle \frac{1}3$ of that value:

$\frac{21}{3}=7$ $\displaystyle \frac{21}{3}=7$

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Example Question #77 : Number Manipulation*

What is the average of $\displaystyle 30$, 6^2 $\displaystyle 6^2$, and $\displaystyle 30$ percent of $\displaystyle 90$?

Possible Answers:

$\displaystyle 32$

$\displaystyle 34$

$\displaystyle 31$

$\displaystyle 28$

Correct answer:

$\displaystyle 31$

Explanation:

First, $6^2=6\cdot6=36$ $\displaystyle 6^2=6\cdot6=36$ and $\displaystyle 30$ percent of $\displaystyle 90$ is $90\cdot.30=27$ $\displaystyle 90\cdot.30=27$.

Then, add up the numbers and divide by the number of numbers to find the average:

$\frac{30+36+27}{3}=31$ $\displaystyle \frac{30+36+27}{3}=31$

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Example Question #76 : How To Manipulate Numbers

What number, divided by $\frac{1}{2}$ $\displaystyle \frac{1}{2}$, is equal to 8^2 $\displaystyle 8^2$?

Possible Answers:

$\displaystyle 28$

$\displaystyle 31$

$\displaystyle 32$

$\displaystyle 33$

Correct answer:

$\displaystyle 32$

Explanation:

First, $8^2=8\cdot8=64$ $\displaystyle 8^2=8\cdot8=64$.

Second, dividing by $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ is the same as multiplying by $\displaystyle 2$. Divide to reverse this:

$64\div2=32$ $\displaystyle 64\div2=32$

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Example Question #79 : Number Manipulation*

What number, multiplied by $\displaystyle 4$, is $\frac{4}{10}$ $\displaystyle \frac{4}{10}$ of $20\%$ $\displaystyle 20\%$ of 500 $\displaystyle 500$$\displaystyle ?$

Possible Answers:

$\displaystyle 40$

$\displaystyle 65$

$\displaystyle 10$

$\displaystyle 25$

Correct answer:

$\displaystyle 10$

Explanation:

Work backwards to solve this problem. First, $\displaystyle 20$ percent of 500 $\displaystyle 500$ is 100 $\displaystyle 100$:

$500\cdot.20=100$ $\displaystyle 500\cdot.20=100$

Then find $\frac{4}{10}$ $\displaystyle \frac{4}{10}$ of that:

$\frac{100\cdot4}{10}=40$ $\displaystyle \frac{100\cdot4}{10}=40$

Finally, divide by $\displaystyle 4$ to reverse the multiplication:

$40\div4=10$ $\displaystyle 40\div4=10$

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All HSPT Quantitative Resources

6 Diagnostic Tests 55 Practice Tests Question of the Day Flashcards Learn by Concept

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HSPT Quantitative : How to manipulate numbers

Study concepts, example questions & explanations for HSPT Quantitative

All HSPT Quantitative Resources

Example Questions

Example Question #71 : How To Manipulate Numbers

Example Question #72 : Number Manipulation*

Example Question #72 : How To Manipulate Numbers

Example Question #73 : How To Manipulate Numbers

Example Question #74 : How To Manipulate Numbers

Example Question #75 : How To Manipulate Numbers

Example Question #76 : Number Manipulation*

Example Question #77 : Number Manipulation*

Example Question #76 : How To Manipulate Numbers

Example Question #79 : Number Manipulation*

All HSPT Quantitative Resources

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