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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 #211 : Number Manipulation*

$A = 100 \times (17+3 )$

$B = 50 \times (17+13 )$

$C = 200 \times (7 - 3)$

Which statement is correct?

Possible Answers:

A < B < C

C < B < A

C < A< B

A < C < B

Correct answer:

C < B < A

Explanation:

By the order of operations, each expression is evaluated by carrying out the operation in parentheses first:

$A = 100 \times (17+3 ) = 100 \times 20 =2,000$

$B = 50 \times (17+13 ) = 50 \times 30 = 1,500$

$C = 200 \times (7 - 3) = 200 \times4 = 800$

Therefore, C < B < A .

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Example Question #211 : How To Manipulate Numbers

What is forty percent of the square of nine?

Possible Answers:

$1\frac{11}{25}$

$12\frac{24}{25}$

$5\frac{1}{16}$

$32 \frac{2}{5}$

Correct answer:

$32 \frac{2}{5}$

Explanation:

The square of nine is $9 ^{2} = 9 \times 9 = 81$ .

Forty percent of a number is equal to the number multiplied by $\frac{40}{100} = \frac{2}{5}$ , so forty percent of 81 is

$\frac{2}{5} \times 81 = \frac{2}{5} \times \frac{81}{1} = \frac{162}{5} = 32 \frac{2}{5}$ .

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Example Question #213 : Number Manipulation*

If twenty is subtracted from a number, the difference is equal to the same number divided by two. What is this number?

Possible Answers:

Correct answer:

Explanation:

If we let be the number in question, "twenty...subtracted from a number" can be rewritten as x - 20 ; "the same number divided by two" can be rewritten as $\frac{x}{2}$ . The two are equal, so we solve the equation

$x - 20 = \frac{x}{2}$

One way to solve this is to first multiply both sides by two to eliminate the fraction:

$2( x - 20) = 2 \cdot \frac{x}{2}$

Distribute:

$2 \cdot x -2 \cdot 20 = x$

2x-40= x

Subtract from, and add 40 to, both sides:

2x-40 - x + 40 = x - x + 40

x= 40 .

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Example Question #212 : How To Manipulate Numbers

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

Possible Answers:

Correct answer:

Explanation:

Work backwards to solve this problem. First, percent of 500 is 100 :

$500\cdot.20=100$

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

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

Finally, divide by to reverse the multiplication:

$40\div4=10$

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Example Question #212 : How To Manipulate Numbers

is percent of what number?

Possible Answers:

Correct answer:

Explanation:

Set up a proportion to solve this problem:

$\frac{32}{x}=\frac{80}{100}$

Cross multiply and solve:

80x=3200

$x=\frac{3200}{80}=40$

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Example Question #213 : How To Manipulate Numbers

What is the difference between 5^3 and 15^2 ?

Possible Answers:

100

Correct answer:

100

Explanation:

First, calculate the exponents:

$5^3=5\cdot5\cdot5=125$

$15^2=15\cdot15=225$

Subtract to find the difference:

225-125=100

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Example Question #215 : How To Manipulate Numbers

What number, when multiplied by , equals the product of and ?

Possible Answers:

Correct answer:

Explanation:

First find the product of and :

$13\cdot12=156$

Then divide by :

$156\div4=39$

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Example Question #216 : How To Manipulate Numbers

What is less than the product of and 710 ?

Possible Answers:

4190

4260

4220

4170

Correct answer:

4190

Explanation:

First, find the product of and 710 :

$6\cdot710=4260$

Then, subtract :

4260-70=4190

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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 #211 : Number Manipulation*

Example Question #211 : How To Manipulate Numbers

Example Question #213 : Number Manipulation*

Example Question #212 : How To Manipulate Numbers

Example Question #212 : How To Manipulate Numbers

Example Question #213 : How To Manipulate Numbers

Example Question #215 : How To Manipulate Numbers

Example Question #216 : How To Manipulate Numbers

All HSPT Quantitative Resources

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