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HSPT Quantitative : How to manipulate numbers

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

Example Questions

Example Question #111 : How To Manipulate Numbers

What is the average of 15^2 $\displaystyle 15^2$, 16^2 $\displaystyle 16^2$, and the product of $\displaystyle 14$ and $\displaystyle 16$?

Possible Answers:

235 $\displaystyle 235$

225 $\displaystyle 225$

210 $\displaystyle 210$

239 $\displaystyle 239$

Correct answer:

235 $\displaystyle 235$

Explanation:

First, calculate each of the three values:

$\displaystyle 15^2=225$

$\displaystyle 16^2=256$

$14\cdot16=224$ $\displaystyle 14\cdot16=224$

Then, find the average by dividing the sum by the number of values:

$\frac{225+256+224}{3}=\frac{705}{3}=235$ $\displaystyle \frac{225+256+224}{3}=\frac{705}{3}=235$

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Example Question #112 : How To Manipulate Numbers

$\displaystyle 42$ is $\displaystyle 20$ percent of what number?

Possible Answers:

810 $\displaystyle 810$

840 $\displaystyle 840$

210 $\displaystyle 210$

284 $\displaystyle 284$

Correct answer:

210 $\displaystyle 210$

Explanation:

Set up a ratio to solve this problem, using an $\displaystyle x$ to represent the unknown value:

$\frac{42}{x}=\frac{20}{100}$ $\displaystyle \frac{42}{x}=\frac{20}{100}$

Then cross multiply and solve:

$42\cdot100=20x$ $\displaystyle 42\cdot100=20x$

$\displaystyle 4200=20x$

$\frac{4200}{20}=x$ $\displaystyle \frac{4200}{20}=x$

210=x $\displaystyle 210=x$

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Example Question #113 : How To Manipulate Numbers

$\displaystyle 44$ is what percent of 400 $\displaystyle 400$?

Possible Answers:

$\displaystyle 20$

$\displaystyle 11$

176 $\displaystyle 176$

17.6 $\displaystyle 17.6$

Correct answer:

$\displaystyle 11$

Explanation:

Set up a ratio to solve this problem:

$\frac{44}{400}=\frac{x}{100}$ $\displaystyle \frac{44}{400}=\frac{x}{100}$

Then cross-multiply and solve:

$44\cdot100=400x$ $\displaystyle 44\cdot100=400x$

$\frac{4400}{400}=11=x$ $\displaystyle \frac{4400}{400}=11=x$

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Example Question #114 : How To Manipulate Numbers

What number, when multiplied by $\displaystyle 2$, is $\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of $\displaystyle 96$?

Possible Answers:

$\displaystyle 24$

$\displaystyle 16$

$\displaystyle 18$

$\displaystyle 19$

Correct answer:

$\displaystyle 16$

Explanation:

First, find $\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of $\displaystyle 96$:

$\frac{96}{3}=32$ $\displaystyle \frac{96}{3}=32$

Then, divide by $\displaystyle 2$:

$32\div2=16$ $\displaystyle 32\div2=16$

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Example Question #115 : How To Manipulate Numbers

What is $\displaystyle 4$ times $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ of $\displaystyle 22$?

Possible Answers:

$\displaystyle 33$

$\displaystyle 44$

$\displaystyle 88$

$\displaystyle 22$

Correct answer:

$\displaystyle 44$

Explanation:

First, $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ of $\displaystyle 22$ is $\displaystyle 11$:

$\frac{22}{2}=11$ $\displaystyle \frac{22}{2}=11$

Next, multiply by $\displaystyle 4$:

$11\cdot4=44$ $\displaystyle 11\cdot4=44$

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Example Question #116 : How To Manipulate Numbers

What is $\displaystyle 30$ percent of 660 $\displaystyle 660$?

Possible Answers:

168 $\displaystyle 168$

212 $\displaystyle 212$

198 $\displaystyle 198$

210 $\displaystyle 210$

Correct answer:

198 $\displaystyle 198$

Explanation:

Multiply by the decimal version of $\displaystyle 30$ percent:

$660\cdot.30=198$ $\displaystyle 660\cdot.30=198$

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Example Question #117 : How To Manipulate Numbers

What is $\displaystyle 6$ less than $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ of $\displaystyle 52$?

Possible Answers:

$\displaystyle 39$

$\displaystyle 33$

$\displaystyle 37$

$\displaystyle 40$

Correct answer:

$\displaystyle 33$

Explanation:

First, find $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ of $\displaystyle 52$:

$\frac{3\cdot52}{4}=39$ $\displaystyle \frac{3\cdot52}{4}=39$

Then subtract $\displaystyle 6$:

39-6=33 $\displaystyle 39-6=33$

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Example Question #118 : How To Manipulate Numbers

What number, multiplied by $\displaystyle 3$, is equal to $\displaystyle 2$ times the square root of $\displaystyle 81$?

Possible Answers:

$\displaystyle 18$

$\displaystyle 12$

$\displaystyle 6$

$\displaystyle 9$

Correct answer:

$\displaystyle 6$

Explanation:

First, find the square root of $\displaystyle 81$:

$\sqrt{81}=9$ $\displaystyle \sqrt{81}=9$

Then, multiply by $\displaystyle 2$:

$9\cdot2=18$ $\displaystyle 9\cdot2=18$

And finally divide by $\displaystyle 3$:

$18\div3=6$ $\displaystyle 18\div3=6$

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Example Question #119 : How To Manipulate Numbers

What is $\displaystyle 14$ percent of 180 $\displaystyle 180$?

Possible Answers:

$\displaystyle 42$

$\displaystyle 45$

25.2 $\displaystyle 25.2$

$\displaystyle 33$

Correct answer:

25.2 $\displaystyle 25.2$

Explanation:

Set up a ratio to solve this problem, representing the unknown value with an $\displaystyle x$:

$\frac{x}{180}=\frac{14}{100}$ $\displaystyle \frac{x}{180}=\frac{14}{100}$

Then cross-multipy and solve:

$180\cdot14=100x$ $\displaystyle 180\cdot14=100x$

$\frac{180\cdot14}{100}=\frac{18\cdot 14}{10}=\frac{9\cdot 14}{5}=\frac{126}{5}=25.2=x$ $\displaystyle \frac{180\cdot14}{100}=\frac{18\cdot 14}{10}=\frac{9\cdot 14}{5}=\frac{126}{5}=25.2=x$

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Example Question #120 : How To Manipulate Numbers

What is the difference between $\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of $\displaystyle 36$ and $\sqrt{36}$ $\displaystyle \sqrt{36}$?

Possible Answers:

$\displaystyle 12$

$\displaystyle 9$

$\displaystyle 3$

$\displaystyle 6$

Correct answer:

$\displaystyle 6$

Explanation:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of $\displaystyle 36$ is

$\frac{36}{3}=12$ $\displaystyle \frac{36}{3}=12$

and $\sqrt{36}$ $\displaystyle \sqrt{36}$ is $\displaystyle 6$ (because $6\cdot6=36$ $\displaystyle 6\cdot6=36$)

Subtract to find the difference:

12-6=6 $\displaystyle 12-6=6$

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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 #111 : How To Manipulate Numbers

Example Question #112 : How To Manipulate Numbers

Example Question #113 : How To Manipulate Numbers

Example Question #114 : How To Manipulate Numbers

Example Question #115 : How To Manipulate Numbers

Example Question #116 : How To Manipulate Numbers

Example Question #117 : How To Manipulate Numbers

Example Question #118 : How To Manipulate Numbers

Example Question #119 : How To Manipulate Numbers

Example Question #120 : How To Manipulate Numbers

All HSPT Quantitative Resources

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