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HSPT Quantitative : HSPT Quantitative Skills

Study concepts, example questions & explanations for HSPT Quantitative

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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 #46 : Non Geometric Comparison

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

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

b) $\frac{6}{18}$ of

c) $\frac{18}{5}$ of

Possible Answers:

b>a>c

b<a<c

a>b>c

a<b<c

Correct answer:

b<a<c

Explanation:

Calculate the expressions to compare the values:

a) $\frac{5}{6}\ of\ 18=\frac{5\cdot18}{6}=15$ $=\frac{5\cdot18}{6}=15$

b) $\frac{6}{18}\ of\ 5=\frac{6\cdot5}{18}=\frac{15}{9}=1\frac{2}{3}$

c) $\frac{18}{5}\ of\ 6= \frac{18\cdot6}{5}=\frac{108}{5}\approx\frac{110}{5}=22$

Notice that (c) is estimated. The real value is slightly lower. We do not need to go through the exact calculation to compare these values, however. It is clear that (b) is smaller than (a), which is smaller than (c).

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Example Question #51 : Non Geometric Comparison

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

a) percent of

b) percent of 160

c) percent of

Possible Answers:

(a) is two times greater than (c)

(a) is two times greater than (b)

(a) is four times greater than (b)

(a) is four times greater than (c)

Correct answer:

(a) is four times greater than (c)

Explanation:

Calculate each expression to compare the values:

a) percent of is:

$80\cdot.60=48$

b) percent of 160 is:

$160\cdot.30=48$

c) percent of is:

$40\cdot.30=12$

(a) and (b) are equal, and (a) is four times greater than (c) because:

$12\cdot4=48$

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Example Question #91 : Hspt Quantitative Skills

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

a) 14x

b) $7x\cdot2x$

c) 7x+2x

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

In (b), the expressions are multiplied. Both the coefficents and variables are multiplied together:

$7x\cdot2x=7\cdot2\cdot x\cdot x = 14x^2$

In (b), the terms are added together. Since they are like terms, the coefficients simply add together:

7x+2x=9x

Now that everything is simplified, we can tell that they are all unequal.

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Example Question #53 : Non Geometric Comparison

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

a) $\frac{2}{3}$ of

b) $\frac{3}{4}$ of

c) $\frac{3}{2}$ of

Possible Answers:

a>b>c

a=b=c

a<b<c

b<a<c

Correct answer:

a<b<c

Explanation:

Calculate each expression to compare the values:

a) $\frac{2}{3}$ of

$\frac{2\cdot18}{3}=12$

b) $\frac{3}{4}$ of

$\frac{3\cdot20}{4}=15$

c) $\frac{3}{2}$ of

$\frac{3\cdot12}{2}=18$

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

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Example Question #92 : Hspt Quantitative Skills

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

a) $\sqrt{16q}$

b) $4\sqrt q$

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

When two elements are multiplied inside of a square root, it is the same as if each of their square roots were multiplied together. Therefore (a) simplifies like this:

$\sqrt{16q}=\sqrt{16}\sqrt{q}=4\sqrt q$

This is equal to (b), but not (c)

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Example Question #55 : Non Geometric Comparison

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

a) 16c^2

b) 4^2c^2

c) (16c)^2

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

Simplify each expression to compare them. Remember for (c) that an exponent outside of parentheses distributes to each of the elements inside:

a) 16c^2

b) 4^2c^2 =16c^2

c) (16c)^2 $=16^2\cdot c^2 = 256c^2$

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

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Example Question #56 : Non Geometric Comparison

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

a) $\frac{7}{8}$

b) percent

Possible Answers:

b>c>a

a<b<c

b<c<a

a>b>c

Correct answer:

a>b>c

Explanation:

Convert each value to a decimal to compare them:

a) $\frac{7}{8}$ =.875

b) percent =.80

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

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Example Question #57 : Non Geometric Comparison

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

a) $11\cdot6$

b) $11\cdot2+11\cdot3$

c) $11\cdot3+11\cdot3$

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 (c) but not (b)

Explanation:

When doing these calculation, be sure to follow the order of operations and do the multiplication before the addition:

a) $11\cdot6=66$

b) $11\cdot2+11\cdot3=22+33=55$

c) $11\cdot3+11\cdot3=33+33=66$

(a) and (c) are both , but (b) is

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Example Question #53 : How To Make Non Geometric Comparisons

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

a) $\frac{7}{8}$

b) $\frac{10}{12}$

c) $\frac{8}{5}$

Possible Answers:

a>b>c

a<b<c

b>a>c

b<a<c

Correct answer:

b<a<c

Explanation:

Choose a common denominator to compare the fractions. One choice is 120 , because its factors include , , and :

a) $\frac{7}{8}\cdot \frac{15}{15}=\frac{105}{120}$

b) $\frac{10}{12}\cdot\frac{10}{10}=\frac{100}{120}$

c) $\frac{8}{5}\cdot\frac{24}{24}=\frac{192}{120}$

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

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Example Question #93 : Hspt Quantitative Skills

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

a) .2x

b) $\frac{2x}{10}$

c) $\frac{1}{5}\cdot x$

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

Both $\frac{2}{10}$ and $\frac{1}{5}$ convert to the same decimal:

Since each of these portions are multiplied by , all expressions are equal.

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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 #46 : Non Geometric Comparison

Example Question #51 : Non Geometric Comparison

Example Question #91 : Hspt Quantitative Skills

Example Question #53 : Non Geometric Comparison

Example Question #92 : Hspt Quantitative Skills

Example Question #55 : Non Geometric Comparison

Example Question #56 : Non Geometric Comparison

Example Question #57 : Non Geometric Comparison

Example Question #53 : How To Make Non Geometric Comparisons

Example Question #93 : Hspt Quantitative Skills

All HSPT Quantitative Resources

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