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HSPT Quantitative : HSPT Quantitative Skills

Study concepts, example questions & explanations for HSPT Quantitative

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

Example Questions

Example Question #12 : How To Manipulate Numbers

What is $\displaystyle 16$ less than the square root of 225 $\displaystyle 225$ ?

Possible Answers:

$\displaystyle 15$

$\displaystyle 9$

$\displaystyle -1$

$\displaystyle -9$

Correct answer:

$\displaystyle -1$

Explanation:

First, the square root of 225 $\displaystyle 225$ is $\displaystyle 15$ because $15\cdot15=225$ $\displaystyle 15\cdot15=225$ .

Second, $\displaystyle 15-16=-1$ .

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Example Question #371 : Hspt Quantitative Skills

What is the difference between 7^2 $\displaystyle 7^2$ and 11^2 $\displaystyle 11^2$ ?

Possible Answers:

$\displaystyle 84$

$\displaystyle 16$

$\displaystyle 52$

$\displaystyle 72$

Correct answer:

$\displaystyle 72$

Explanation:

First, square the numbers:

$7^2=7\cdot7=49$ $\displaystyle 7^2=7\cdot7=49$

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

Then, subtract to find the difference:

$\displaystyle 121-49=72$

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Example Question #372 : Hspt Quantitative Skills

What is the average of $\displaystyle 34$ , 8^2 $\displaystyle 8^2$ , and $\displaystyle 7$ ?

Possible Answers:

$\displaystyle 35$

$\displaystyle 43$

$\displaystyle 26$

$\displaystyle 62$

Correct answer:

$\displaystyle 35$

Explanation:

First, $8^2=8\cdot8=64$ $\displaystyle 8^2=8\cdot8=64$ .

Then, find the sum and divide by the number of elements:

$\frac{34+64+7}{3}=\frac{105}{3}=35$ $\displaystyle \frac{34+64+7}{3}=\frac{105}{3}=35$

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Example Question #373 : Hspt Quantitative Skills

$\displaystyle 16$ is $\displaystyle 48$ percent of what number divided by $\displaystyle 3$ ?

Possible Answers:

$\frac{1}3{}$ $\displaystyle \frac{1}3{}$

122 $\displaystyle 122$

$\displaystyle 23$

100 $\displaystyle 100$

Correct answer:

100 $\displaystyle 100$

Explanation:

First, find the number that $\displaystyle 16$ is $\displaystyle 48$ percent of. We will call that unknown number $\displaystyle x$ :

$16=.48\cdot x$ $\displaystyle 16=.48\cdot x$

$x=16\div.48=33\frac{1}{3}$ $\displaystyle x=16\div.48=33\frac{1}{3}$

Then, multiply by three to reverse the division:

$33\frac{1}{3}\cdot3=100$ $\displaystyle 33\frac{1}{3}\cdot3=100$

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Example Question #374 : Hspt Quantitative Skills

$\displaystyle 46$ is what percent of 575 $\displaystyle 575$ ?

Possible Answers:

$\displaystyle 16$

$\displaystyle 26$

$\displaystyle 8$

$\displaystyle 5$

Correct answer:

$\displaystyle 8$

Explanation:

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

Divide both sides by 575 $\displaystyle 575$ to find $\displaystyle x$ :

$x=46\div575=.08$ $\displaystyle x=46\div575=.08$

Rewritten as a percent, $\displaystyle .08$ is $\displaystyle 8$ percent.

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Example Question #375 : Hspt Quantitative Skills

What is the ratio of the circumference of a circle with a radius of $\displaystyle 5$ to the circumference of a circle with a radius of $\displaystyle 10$ ?

Possible Answers:

1:2 $\displaystyle 1:2$

2:3 $\displaystyle 2:3$

2:5 $\displaystyle 2:5$

1:4 $\displaystyle 1:4$

Correct answer:

1:2 $\displaystyle 1:2$

Explanation:

The formula for circumference is $c=2\pi r$ $\displaystyle c=2\pi r$ .

For the first circle:

$c=2\cdot\pi\cdot 5 = 10\pi$ $\displaystyle c=2\cdot\pi\cdot 5 = 10\pi$

And for the second:

$c=2\cdot\pi \cdot 10=20\pi$ $\displaystyle c=2\cdot\pi \cdot 10=20\pi$

The ratio is then 10:20 $\displaystyle 10:20$ , or 1:2 $\displaystyle 1:2$ .

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Example Question #376 : Hspt Quantitative Skills

What is $\displaystyle 30$ percent of the product of $\displaystyle 6$ and $\displaystyle 30$ ?

Possible Answers:

$\displaystyle 66$

$\displaystyle 54$

$\displaystyle 6$

$\displaystyle 42$

Correct answer:

$\displaystyle 54$

Explanation:

Work backwards to solve this problem. First, the product of $\displaystyle 6$ and $\displaystyle 30$ is:

$6\cdot30 = 180$ $\displaystyle 6\cdot30 = 180$

Second, $\displaystyle 30$ percent of that is:

$180\cdot.30=54$ $\displaystyle 180\cdot.30=54$

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Example Question #377 : Hspt Quantitative Skills

What number is $\displaystyle 16$ more than $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ of $\displaystyle 28$ ?

Possible Answers:

$\displaystyle 22$

$\displaystyle 30$

$\displaystyle 14$

$\displaystyle 32$

Correct answer:

$\displaystyle 30$

Explanation:

First, $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ of $\displaystyle 28$ is $\displaystyle 14$ , because $28\div2=14$ $\displaystyle 28\div2=14$ .

Then, add $\displaystyle 16$ :

$\displaystyle 14+16=30$

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Example Question #378 : Hspt Quantitative Skills

What number divided by $\displaystyle 3$ equals $\frac{1}{4}$ $\displaystyle \frac{1}{4}$ of 120 $\displaystyle 120$ ?

Possible Answers:

$\displaystyle 90$

$\displaystyle 40$

$\displaystyle 80$

110 $\displaystyle 110$

Correct answer:

$\displaystyle 90$

Explanation:

First, $\frac{1}{4}$ $\displaystyle \frac{1}{4}$ of 120 $\displaystyle 120$ is $\displaystyle 30$ because $120\div4=30$ $\displaystyle 120\div4=30$ .

Then, multiply by $\displaystyle 3$ to reverse the division:

$30\cdot3=90$ $\displaystyle 30\cdot3=90$

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Example Question #379 : Hspt Quantitative Skills

What number is twice as much as the square root of $\displaystyle 81$ ?

Possible Answers:

$\displaystyle 18$

$\displaystyle 9$

$\displaystyle 16$

$\displaystyle 22$

Correct answer:

$\displaystyle 18$

Explanation:

The square root of $\displaystyle 81$ is $\displaystyle 9$ because $9\cdot9=81$ $\displaystyle 9\cdot9=81$ . Next, multiply by $\displaystyle 2$ to find twice as much:

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

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All HSPT Quantitative Resources

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

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HSPT Quantitative : HSPT Quantitative Skills

Study concepts, example questions & explanations for HSPT Quantitative

All HSPT Quantitative Resources

Example Questions

Example Question #12 : How To Manipulate Numbers

Example Question #371 : Hspt Quantitative Skills

Example Question #372 : Hspt Quantitative Skills

Example Question #373 : Hspt Quantitative Skills

Example Question #374 : Hspt Quantitative Skills

Example Question #375 : Hspt Quantitative Skills

Example Question #376 : Hspt Quantitative Skills

Example Question #377 : Hspt Quantitative Skills

Example Question #378 : Hspt Quantitative Skills

Example Question #379 : Hspt Quantitative Skills

All HSPT Quantitative Resources

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