How to manipulate numbers - HSPT Quantitative

Card 0 of 20

Question

What number is the square of 4 divided by 2?

Answer

First, square 4.

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

Then divide the answer by two.

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

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Question

What number is the cube of 4 multiplied by 2?

Answer

First, cube 4.

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

Multiply that answer by 2.

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

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Question

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

Answer

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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Question

What number added to 15 gives you $\dpi{100} \frac{1}{4}$ of 72 ?

Answer

Set up an equation using the information provided.

$\dpi{100} 15+x=\frac{1}{4}\cdot 72$

$\dpi{100} 15+x=18$

$\dpi{100} 15+x-15=18-15$

$\dpi{100} x=3$

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Question

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

Answer

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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Question

What number divided by is percent of ?

Answer

Work backwards to solve this problem. First, 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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Question

What number is $\frac{2}{15}$ of the average of , , and ?

Answer

Work backwards to solve this problem. First, the average of , , and is , because $\frac{105+110+280}{3}=165$ .

Next, find $\frac{2}{15}$ of this number by dividing by and multiplying by :

$165\div 15=11$

$11\cdot 2=22$

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Question

What number is less than the product of $4^{2}$ and $2^{3}$ ?

Answer

Work backwards to solve this problem. First, $4^{2}=16$ and $2^{3}=8$ .

The product of these is , because $16\cdot 8=128$ .

Finally, less than is , because .

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Question

percent of percent of is what number?

Answer

percent of is , because $300\cdot .15=45$ .

percent of is , because $45\cdot .80=36$ .

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Question

is percent of what number?

Answer

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

$72\div .30=240$

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Question

$\frac{3}{4}$ of what number is $\frac{1}{3}$ of ?

Answer

$\frac{1}{3}$ of is , because $27\div 3=9$ .

Then, $\frac{3}{4}$ of is , because $\frac{9}{\frac{3}{4}}=9\cdot\frac{4}{3}=12$ .

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Question

What number is less than the product of , , and $\frac{5}{8}$ ?

Answer

Work backwards to solve this problem. First, find the product of the three numbers:

$4\cdot14\cdot\frac{5}{8}=35$

Second, subtract .

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Question

What number is percent of the difference between and ?

Answer

Work backwards to solve this problem. First, find the difference between the two numbers through subtraction:

Then, multiply by to find the answer:

$84\cdot.75=63$

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Question

What number when divided by is the sum of , , and ?

Answer

Find the sum of the three numbers through addition:

Then, multiply by to reverse the division:

$1\cdot6=6$

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Question

What number is percent of the difference between and ?

Answer

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

Then, percent of that is :

$40\cdot.35=14$

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Question

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

Answer

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

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

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

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Question

What number is percent of ?

Answer

Multiply by to find percent:

$225\cdot.28=63$

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Question

What number, when divided by the product of and , equals the square root of ?

Answer

Work backwards to solve this problem. First, the product of and is :

$16\cdot3.5=56$

Next, the square root of is :

$\sqrt{9}=3$

Now, the question is, "What number, when divided by , equals ?" This can also be written as:

$\frac{x}{56}=3$

Multiply both sides by to find :

$x=56\cdot3=168$

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Question

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

Answer

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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Question

is what percent of ?

Answer

Using to represent the unknown percentage, we can say that $575\cdot x = 46$ .

Divide both sides by to find :

$x=46\div575=.08$

Rewritten as a percent, is percent.

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