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HSPT Quantitative : HSPT Quantitative Skills

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All HSPT Quantitative Resources

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

Example Questions

Example Question #111 : Hspt Quantitative Skills

Examine (a), (b), and (c) to find the best answer:

a) $\displaystyle .02$ percent

b) $\displaystyle .2$

c) $\frac{2}{100}$ $\displaystyle \frac{2}{100}$

Possible Answers:

a<c<b $\displaystyle a< c< b$

b=c>a $\displaystyle b=c>a$

a=b<c $\displaystyle a=b< c$

a>c>b $\displaystyle a>c>b$

Correct answer:

a<c<b $\displaystyle a< c< b$

Explanation:

Convert each to a decimal in order to compare them:

a) $\displaystyle .0002$

b) $\displaystyle .2$

c) $\displaystyle .02$

It is now evident that (a) is smaller than (c), which is smaller than (b).

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Example Question #112 : Hspt Quantitative Skills

Examine (a), (b), and (c) to find the best answer:

a) $\frac{\sqrt{2}}{3}$ $\displaystyle \frac{\sqrt{2}}{3}$

b) $\frac{\sqrt{2}}{\sqrt{3}}$ $\displaystyle \frac{\sqrt{2}}{\sqrt{3}}$

c) $\sqrt{\frac{2}{3}}$ $\displaystyle \sqrt{\frac{2}{3}}$

Possible Answers:

(b) is equal to (c) but not (a)

(b) is equal to (a) but not (c)

(a), (b), and (c) are all unequal

(a), (b), and (c) are all equal

Correct answer:

(b) is equal to (c) but not (a)

Explanation:

The property of exponents to remember here is that $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$ $\displaystyle \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$.

This explains why (b) and (c) are equal. (a) cannot be equal because $\sqrt{3}\neq3$ $\displaystyle \sqrt{3}\neq3$.

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Example Question #113 : Hspt Quantitative Skills

Examine (a), (b), and (c) to find the best answer:

a) $\frac{x+x\cdot5}{20}$ $\displaystyle \frac{x+x\cdot5}{20}$

b) $\frac{x+x}{4}$ $\displaystyle \frac{x+x}{4}$

c) $\frac{3x}{10}$ $\displaystyle \frac{3x}{10}$

Possible Answers:

(a) is equal to (c) but not (b)

(a), (b), and (c) are all unequal

(a) is equal to (b) but not (c)

(a), (b), and (c) are all equal

Correct answer:

(a) is equal to (c) but not (b)

Explanation:

Following the order of operations, (a) simplifies to be (c):

$\frac{x+x\cdot5}{20}=\frac{x+5x}{20}=\frac{6x}{20}=\frac{3x}{10}$ $\displaystyle \frac{x+x\cdot5}{20}=\frac{x+5x}{20}=\frac{6x}{20}=\frac{3x}{10}$

(b) simplifies to the following:

$\frac{x+x}{4}=\frac{2x}{4}=\frac{x}{2}$ $\displaystyle \frac{x+x}{4}=\frac{2x}{4}=\frac{x}{2}$

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Example Question #114 : Hspt Quantitative Skills

Examine (a), (b), and (c) to find the best answer:

a) $\frac{5}{6}$ $\displaystyle \frac{5}{6}$

b) $\frac{29}{36}$ $\displaystyle \frac{29}{36}$

c) $\frac{4}{9}$ $\displaystyle \frac{4}{9}$

Possible Answers:

a=b=c $\displaystyle a=b=c$

a=b>c $\displaystyle a=b>c$

a<b<c $\displaystyle a< b< c$

a>b>c $\displaystyle a>b>c$

Correct answer:

a>b>c $\displaystyle a>b>c$

Explanation:

Find a common denominator to compare the fractions. Here, we use $\displaystyle 36$:

a) $\frac{5}{6}=\frac{30}{36}$ $\displaystyle \frac{5}{6}=\frac{30}{36}$

b) $\frac{29}{36}$ $\displaystyle \frac{29}{36}$

c) $\frac{4}{9}=\frac{16}{36}$ $\displaystyle \frac{4}{9}=\frac{16}{36}$

It is now evident that (a) is greater than (b), which is greater than (c).

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Example Question #115 : Hspt Quantitative Skills

Examine (a), (b), and (c) to find the best answer:

a) 12x^2 $\displaystyle 12x^2$

b) $\displaystyle 3x^2+9x^2$

c) $3x\cdot4x$ $\displaystyle 3x\cdot4x$

Possible Answers:

(a), (b), and (c) are all unequal

(a), (b), and (c) are all equal

(a) equals (c) but not (b)

(a) equals (b) but not (c)

Correct answer:

(a), (b), and (c) are all equal

Explanation:

(a) is a simplified version of both (b) and (c). For (b), you can add the like terms together and end up with (a). For (c), you can multiply the constants and the variables together and also end up with (a). To test this, try substituting a number in for $\displaystyle x$.

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Example Question #116 : Hspt Quantitative Skills

Examine (a), (b), and (c) to find the best answer:

a) $\displaystyle (7-x) ^2$

b) $\displaystyle (7-x)(7-x)$

c) 49-x^2 $\displaystyle 49-x^2$

Possible Answers:

(a), (b), and (c) are all equal

(a) is equal to (c) but not (b)

(a), (b), and (c) are all unequal

(a) is equal to (b) but not (c)

Correct answer:

(a) is equal to (b) but not (c)

Explanation:

Test this problem by substituting a number in for $\displaystyle x$. For example, here is x=2 $\displaystyle x=2$:

a) $\displaystyle (7-2)^2=5^2=25$

b) $\displaystyle (7-2)(7-2)=(5)(5)=25$

c) $\displaystyle 49-2^2=49-4=45$

It is evident that (a) and (b) are equal but (c) is not.

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Example Question #76 : How To Make Non Geometric Comparisons

Examine (a), (b), and (c) to find the best answer:

a) $\displaystyle 5$ percent

b) $\displaystyle .5$

c) $\frac{1}{5}$ $\displaystyle \frac{1}{5}$

Possible Answers:

a=b<c $\displaystyle a=b< c$

a=b=c $\displaystyle a=b=c$

a<c<b $\displaystyle a< c< b$

a>c>b $\displaystyle a>c>b$

Correct answer:

a<c<b $\displaystyle a< c< b$

Explanation:

Convert all of the values into decimals to compare them:

a) $\displaystyle 5$ percent =.05 $\displaystyle =.05$

b) $\displaystyle .5$

c) $\frac{1}{5}=.2$ $\displaystyle \frac{1}{5}=.2$

It is now evident that (a) is smaller than (c), which is smaller than (b)

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Example Question #117 : Hspt Quantitative Skills

Examine (a), (b), and (c) to find the best answer:

a) $\displaystyle 7$ percent of $\displaystyle q$

b) .07q $\displaystyle .07q$

c) .7q $\displaystyle .7q$

Possible Answers:

(a), (b), and (c) are all unequal

(a), (b), and (c) are all equal

(a) is equal to (c) but not (b)

(a) is equal to (b) but not (c)

Correct answer:

(a) is equal to (b) but not (c)

Explanation:

To find the percent of a number, in this case $\displaystyle q$, multiply by the percent over one hundred:

$\frac{7}{100}q=.07q$ $\displaystyle \frac{7}{100}q=.07q$

Therefore, (a) and (b) are equal. .7q $\displaystyle .7q$ would be $\displaystyle 70$ percent.

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Example Question #78 : How To Make Non Geometric Comparisons

Examine (a), (b), and (c) to find the best answer:

a) $\displaystyle .01$ percent of $\displaystyle x$

b) .01x $\displaystyle .01x$

c) .0001x $\displaystyle .0001x$

Possible Answers:

(a) is equal to (b) but not (c)

(a), (b), and (c) are all unequal

(a), (b), and (c) are all equal

(a) is equal to (c) but not (b)

Correct answer:

(a) is equal to (c) but not (b)

Explanation:

To find a percentage of the number, multiply it by the decimal version of the percent, or the percent divided by 100 $\displaystyle 100$.

Therefore, $\displaystyle .01$ percent of $\displaystyle x$ is equal to $\frac{.01}{100}x$ $\displaystyle \frac{.01}{100}x$, or .0001x $\displaystyle .0001x$

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Example Question #79 : How To Make Non Geometric Comparisons

Exmaine (a), (b), and (c) to find the best answer:

a) $\frac{9}{10}$ $\displaystyle \frac{9}{10}$ of $\displaystyle 4$

b) $\frac{10}{4}$ $\displaystyle \frac{10}{4}$ of $\displaystyle 9$

c) $\frac{4}{9}$ $\displaystyle \frac{4}{9}$ of $\displaystyle 10$

Possible Answers:

a<c<b $\displaystyle a< c< b$

a<b<c $\displaystyle a< b< c$

a>c>b $\displaystyle a>c>b$

a=b=c $\displaystyle a=b=c$

Correct answer:

a<c<b $\displaystyle a< c< b$

Explanation:

Multiply out each expression to compare the values:

a) $\frac{9\cdot4}{10}=3.6$ $\displaystyle \frac{9\cdot4}{10}=3.6$

b) $\frac{10\cdot9}{4}=22.5$ $\displaystyle \frac{10\cdot9}{4}=22.5$

c) $\frac{4\cdot10}{9}=4.\overline{44}$ $\displaystyle \frac{4\cdot10}{9}=4.\overline{44}$

It is now evident that (a) is smaller than (c), which is smaller than (b)

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All HSPT Quantitative Resources

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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 #111 : Hspt Quantitative Skills

Example Question #112 : Hspt Quantitative Skills

Example Question #113 : Hspt Quantitative Skills

Example Question #114 : Hspt Quantitative Skills

Example Question #115 : Hspt Quantitative Skills

Example Question #116 : Hspt Quantitative Skills

Example Question #76 : How To Make Non Geometric Comparisons

Example Question #117 : Hspt Quantitative Skills

Example Question #78 : How To Make Non Geometric Comparisons

Example Question #79 : How To Make Non Geometric Comparisons

All HSPT Quantitative Resources

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