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HSPT Quantitative : How to manipulate numbers

Study concepts, example questions & explanations for HSPT Quantitative

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Example Questions

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Example Question #1 : Number Manipulation*

What number is the square of 4 divided by 2?

Possible Answers:

$\dpi{100} 4$

$\dpi{100} 16$

$\dpi{100} 1$

$\dpi{100} 8$

Correct answer:

$\dpi{100} 8$

Explanation:

First, square 4.

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

Then divide the answer by two.

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

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Example Question #1 : Number Manipulation*

What number is the cube of 4 multiplied by 2?

Possible Answers:

$\dpi{100} 24$

$\dpi{100} 64$

$\dpi{100} 128$

$\dpi{100} 32$

Correct answer:

$\dpi{100} 128$

Explanation:

First, cube 4.

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

Multiply that answer by 2.

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

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Example Question #1 : How To Manipulate Numbers

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

Possible Answers:

$\dpi{100} 40$

$\dpi{100} 25$

$\dpi{100} 5$

$\dpi{100} 20$

Correct answer:

$\dpi{100} 25$

Explanation:

Set up an equation that fits the information:

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

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

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

$\dpi{100} x=25$

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Example Question #2 : Number Manipulation*

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

Possible Answers:

$\dpi{100} 20$

$\dpi{100} 32$

$\dpi{100} 3200$

$\dpi{100} 40$

Correct answer:

$\dpi{100} 40$

Explanation:

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

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

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

$\dpi{100} x=40$

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Example Question #2 : How To Manipulate Numbers

What number divided by is 150 percent of ?

Possible Answers:

180

Correct answer:

180

Explanation:

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

Now, multiply this by to reverse the division.

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

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Example Question #1 : How To Manipulate Numbers

is percent of what number?

Possible Answers:

360

240

216

Correct answer:

240

Explanation:

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

$72\div .30=240$

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Example Question #1 : How To Manipulate Numbers

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

Possible Answers:

Correct answer:

Explanation:

Work backwards to solve this problem. First, less than 101 is :

101-5=96

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

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

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Example Question #2 : How To Manipulate Numbers

What number is percent of the difference between 153 and 113 ?

Possible Answers:

114

Correct answer:

Explanation:

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

153-113=40

Then, percent of that is :

$40\cdot.35=14$

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Example Question #1 : Number Manipulation*

What number is percent of 225 ?

Possible Answers:

900

Correct answer:

Explanation:

Multiply 225 by to find percent:

$225\cdot.28=63$

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Example Question #2 : Number Manipulation*

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

Possible Answers:

101

104

202

Correct answer:

101

Explanation:

The first step is to calculate the squares:

$9^2=9\cdot9=81$

$11^2=11\cdot11=121$

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

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

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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 : Number Manipulation*

Example Question #1 : Number Manipulation*

Example Question #1 : How To Manipulate Numbers

Example Question #2 : Number Manipulation*

Example Question #2 : How To Manipulate Numbers

Example Question #1 : How To Manipulate Numbers

Example Question #1 : How To Manipulate Numbers

Example Question #2 : How To Manipulate Numbers

Example Question #1 : Number Manipulation*

Example Question #2 : Number Manipulation*

All HSPT Quantitative Resources

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