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HSPT Quantitative : How to manipulate numbers

Study concepts, example questions & explanations for HSPT Quantitative

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Example Questions

Example Question #1 : How To Manipulate Numbers

What number is the square of 4 divided by 2?

Possible Answers:

$\dpi{100} 1$ $\displaystyle \dpi{100} 1$

$\dpi{100} 16$ $\displaystyle \dpi{100} 16$

$\dpi{100} 8$ $\displaystyle \dpi{100} 8$

$\dpi{100} 4$ $\displaystyle \dpi{100} 4$

Correct answer:

$\dpi{100} 8$ $\displaystyle \dpi{100} 8$

Explanation:

First, square 4.

$\dpi{100} 4^{2}=16$ $\displaystyle \dpi{100} 4^{2}=16$

Then divide the answer by two.

$\dpi{100} \frac{16}{2}=8$ $\displaystyle \dpi{100} \frac{16}{2}=8$

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Example Question #2 : How To Manipulate Numbers

What number is the cube of 4 multiplied by 2?

Possible Answers:

$\dpi{100} 32$ $\displaystyle \dpi{100} 32$

$\dpi{100} 24$ $\displaystyle \dpi{100} 24$

$\dpi{100} 128$ $\displaystyle \dpi{100} 128$

$\dpi{100} 64$ $\displaystyle \dpi{100} 64$

Correct answer:

$\dpi{100} 128$ $\displaystyle \dpi{100} 128$

Explanation:

First, cube 4.

$\dpi{100} 4^{3}=64$ $\displaystyle \dpi{100} 4^{3}=64$

Multiply that answer by 2.

$\dpi{100} 2\times 64=128$ $\displaystyle \dpi{100} 2\times 64=128$

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Example Question #1 : Number Manipulation*

What number divided by 5 is $\dpi{100} \frac{1}{8}$ $\displaystyle \dpi{100} \frac{1}{8}$ of 40?

Possible Answers:

$\dpi{100} 25$ $\displaystyle \dpi{100} 25$

$\dpi{100} 40$ $\displaystyle \dpi{100} 40$

$\dpi{100} 5$ $\displaystyle \dpi{100} 5$

$\dpi{100} 20$ $\displaystyle \dpi{100} 20$

Correct answer:

$\dpi{100} 25$ $\displaystyle \dpi{100} 25$

Explanation:

Set up an equation that fits the information:

$\dpi{100} \frac{x}{5}=\frac{1}{8}\cdot 40$ $\displaystyle \dpi{100} \frac{x}{5}=\frac{1}{8}\cdot 40$

$\dpi{100} \frac{x}{5}=5$ $\displaystyle \dpi{100} \frac{x}{5}=5$

$\dpi{100} 5\cdot \frac{x}{5}=5\cdot 5$ $\displaystyle \dpi{100} 5\cdot \frac{x}{5}=5\cdot 5$

$\dpi{100} x=25$ $\displaystyle \dpi{100} x=25$

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Example Question #3 : How To Manipulate Numbers

What number is 4 times $\dpi{100} \frac{1}{8}$ $\displaystyle \dpi{100} \frac{1}{8}$ of 80?

Possible Answers:

$\dpi{100} 20$ $\displaystyle \dpi{100} 20$

$\dpi{100} 32$ $\displaystyle \dpi{100} 32$

$\dpi{100} 3200$ $\displaystyle \dpi{100} 3200$

$\dpi{100} 40$ $\displaystyle \dpi{100} 40$

Correct answer:

$\dpi{100} 40$ $\displaystyle \dpi{100} 40$

Explanation:

Set up an equation using the information provided, and then solve.

$\dpi{100} x=4\cdot (\frac{1}{8}\cdot 80)$ $\displaystyle \dpi{100} x=4\cdot (\frac{1}{8}\cdot 80)$

$\dpi{100} x=4\cdot 10$ $\displaystyle \dpi{100} x=4\cdot 10$

$\dpi{100} x=40$ $\displaystyle \dpi{100} x=40$

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Example Question #2 : Number Manipulation*

What number divided by $\displaystyle 2$ is 150 $\displaystyle 150$ percent of $\displaystyle 60$?

Possible Answers:

$\displaystyle 90$

180 $\displaystyle 180$

$\displaystyle 85$

$\displaystyle 45$

Correct answer:

180 $\displaystyle 180$

Explanation:

Work backwards to solve this problem. First, 150 $\displaystyle 150$ percent of $\displaystyle 60$ is $\displaystyle 90$, because $1.50\cdot 60=90$ $\displaystyle 1.50\cdot 60=90$.

Now, multiply this by $\displaystyle 2$ to reverse the division.

$90\cdot 2=180$ $\displaystyle 90\cdot 2=180$, so the answer is 180.

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Example Question #6 : How To Manipulate Numbers

$\displaystyle 72$ is $\displaystyle 30$ percent of what number?

Possible Answers:

216 $\displaystyle 216$

240 $\displaystyle 240$

360 $\displaystyle 360$

$\displaystyle 22$

Correct answer:

240 $\displaystyle 240$

Explanation:

Using $\displaystyle z$ to represent the unknown number, we know that .30z=72 $\displaystyle .30z=72$. Using algebraic manipulation, divide both sides by $\displaystyle .30$ to find $\displaystyle z$.

$72\div .30=240$ $\displaystyle 72\div .30=240$

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Example Question #7 : How To Manipulate Numbers

What number is $\frac{2}{3}$ $\displaystyle \frac{2}{3}$ of $\displaystyle 5$ less than 101 $\displaystyle 101$?

Possible Answers:

$\displaystyle 64$

$\displaystyle 71$

$\displaystyle 96$

$\displaystyle 60$

Correct answer:

$\displaystyle 64$

Explanation:

Work backwards to solve this problem. First, $\displaystyle 5$ less than 101 $\displaystyle 101$ is $\displaystyle 96$:

$\displaystyle 101-5=96$

Then, $\frac{2}{3}$ $\displaystyle \frac{2}{3}$ of $\displaystyle 96$ is $\displaystyle 64$:

$96\cdot\frac{2}{3}=64$ $\displaystyle 96\cdot\frac{2}{3}=64$

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Example Question #8 : How To Manipulate Numbers

What number is $\displaystyle 35$ percent of the difference between 153 $\displaystyle 153$ and 113 $\displaystyle 113$?

Possible Answers:

114 $\displaystyle 114$

$\displaystyle 54$

$\displaystyle 14$

$\displaystyle 40$

Correct answer:

$\displaystyle 14$

Explanation:

Work backwards to solve this problem. First, the difference between 153 $\displaystyle 153$ and 113 $\displaystyle 113$ is $\displaystyle 40$:

$\displaystyle 153-113=40$

Then, $\displaystyle 35$ percent of that is $\displaystyle 14$:

$40\cdot.35=14$ $\displaystyle 40\cdot.35=14$

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Example Question #6 : How To Manipulate Numbers

What number is $\displaystyle 28$ percent of 225 $\displaystyle 225$?

Possible Answers:

$\displaystyle 72$

$\displaystyle 63$

$\displaystyle 54$

900 $\displaystyle 900$

Correct answer:

$\displaystyle 63$

Explanation:

Multiply 225 $\displaystyle 225$ by $\displaystyle .28$ to find $\displaystyle 28$ percent:

$225\cdot.28=63$ $\displaystyle 225\cdot.28=63$

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Example Question #3 : How To Manipulate Numbers

What is the average of $9^{2}$ $\displaystyle 9^{2}$ and $11^{2}$ $\displaystyle 11^{2}$?

Possible Answers:

$\displaystyle 92$

202 $\displaystyle 202$

101 $\displaystyle 101$

104 $\displaystyle 104$

Correct answer:

101 $\displaystyle 101$

Explanation:

The first step is to calculate the squares:

$9^2=9\cdot9=81$ $\displaystyle 9^2=9\cdot9=81$

$11^2=11\cdot11=121$ $\displaystyle 11^2=11\cdot11=121$

Second, find the average by finding the sum and dividing by the number of numbers:

$\frac{81+121}{2}=\frac{202}{2}=101$ $\displaystyle \frac{81+121}{2}=\frac{202}{2}=101$

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All HSPT Quantitative Resources

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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 #1 : How To Manipulate Numbers

Example Question #2 : How To Manipulate Numbers

Example Question #1 : Number Manipulation*

Example Question #3 : How To Manipulate Numbers

Example Question #2 : Number Manipulation*

Example Question #6 : How To Manipulate Numbers

Example Question #7 : How To Manipulate Numbers

Example Question #8 : How To Manipulate Numbers

Example Question #6 : How To Manipulate Numbers

Example Question #3 : How To Manipulate Numbers

All HSPT Quantitative Resources

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