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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

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Example Question #41 : How To Make Geometric Comparisons

Find the relationship between the areas of the following shapes.

a. A square of side length

b. A parallelogram of base and height $\frac{1}{2}$

c. A triangle with base and height

Possible Answers:

a=b<c

b>a>c

a>b>c

a>b=c

a=b=c

Correct answer:

a=b=c

Explanation:

First, find the areas.

a=s^2=(1)^2=1

$b=(b)(h)=(2)*(\tfrac{1}{2})=1$

$c=\tfrac{1}{2}(b)(h)=(\tfrac{1}{2})(1)(2)=1$

The correct choice is a=b=c .

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Example Question #1 : How To Make Non Geometric Comparisons

$\dpi{100} \frac{1}{3}$ of what number is equal to 2 times 4?

Possible Answers:

$\dpi{100} 15$

$\dpi{100} 24$

$\dpi{100} 12$

$\dpi{100} 30$

Correct answer:

$\dpi{100} 24$

Explanation:

Set up the following equation.

$\dpi{100} \frac{1}{3}x=2\cdot 4$

$\dpi{100} \frac{1}{3}x=8$

$\dpi{100} 3\cdot \frac{1}{3}x=8\cdot 3$

$\dpi{100} x=24$

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Example Question #1 : Non Geometric Comparison

Examine (A), (B), and (C) and find the best answer.

(A) $\dpi{100} .75$

(B) $\dpi{100} \frac{1}{2}$ of $\dpi{100} 1.5$

Possible Answers:

(A) and (C) are equal and are greater than (B)

(A), (B), and (C) are equal.

(B) is less than (A), which is less than (C).

Correct answer:

(A), (B), and (C) are equal.

Explanation:

All of these choices are equal.

$\dpi{100} \frac{3}{4}$ is .75 in fraction form, and .75 is $\dpi{100} \frac{3}{4}$ in decimal form.

$\dpi{100} \frac{1}{2}$ of 1.5 is the same as $\dpi{100} \frac{1}{2}\cdot \frac{3}{2}=\frac{3}{4}$ .

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Example Question #2 : Non Geometric Comparison

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

a) the square root of 121

b) $\frac{1}{20}$ of 200

c) the average of &

Possible Answers:

a>b=c

a<b<c

a>b>c

a=b=c

Correct answer:

a>b=c

Explanation:

a) The square root of 121 is , because $11\cdot 11=121$ .

b) $\frac{1}{20}$ of 200 is , because $200\div 20=10$ .

c) The average of and is , because $\frac{5+15}{2}=10$ .

Therefore (b) and (c) are equal, and they are both smaller than (a).

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Example Question #1 : Non Geometric Comparison

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

a) percent of

b) percent of 120

c) percent of 110

Possible Answers:

a<b<c

a=b<c

b<a<c

a=b=c

Correct answer:

b<a<c

Explanation:

a) percent of is because $96\cdot .50=48$ .

b) percent of 120 is because $120\cdot .30=40$ .

c) percent of 110 is because $111\cdot .60=66$ .

Therefore (b) is smaller than (a) which is smaller than (c).

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Example Question #1 : How To Make Non Geometric Comparisons

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

b) 2(2+3)

c) $\frac{2}{(2+3)}$

Possible Answers:

a>b>c

a<b=c

a<b<c

a=b=c

Correct answer:

a>b>c

Explanation:

b) 2(2+3) $= 2\cdot 5 = 10$

c) $\frac{2}{(2+3)}$ $=\frac{2}{5}= .4$

Therefore (a) is larger than (b) which is larger than (c).

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Example Question #2 : How To Make Non Geometric Comparisons

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

a) $4^{2}$

b) $2^{4}$

c) $2^{2} + 4$

Possible Answers:

a=b=c

a>b>c

a=b>c

a<b<c

Correct answer:

a=b>c

Explanation:

a) $4^{2} = 4\cdot 4 =16$

b) $2^{4} = 2\cdot 2\cdot 2\cdot 2 = 16$

c) $2^{2} + 4 = 2\cdot 2 + 4 = 4+4 = 8$

Therefore (a) and (b) are equal, and they are larger than (c).

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Example Question #1 : How To Make Non Geometric Comparisons

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

a) $5+\frac{6+8}{2}$

b) $\frac{5(6+8)}{2}$

c) $\frac{5}{2}\cdot6+8$

Possible Answers:

b>c>a

a=b=c

a=b>c

a>b>c

Correct answer:

b>c>a

Explanation:

This question tests your understanding of the order of operations. First complete operations in parentheses, then multiplication and division, and finally addition and subtraction.

a) $5+\frac{6+8}{2} = 5+\frac{14}{2} = 5+7 = 12$

b) $\frac{5(6+8)}{2}=\frac{5\cdot 14}{2}=\frac{70}{2}=35$

c) $\frac{5}{2}\cdot6+8=2.5\cdot6+8=15+8=23$

Therefore (a) is smaller than (c) which is smaller than (b).

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Example Question #8 : Non Geometric Comparison

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

a) $\sqrt{64}$

b) percent of

c) $\frac{64}{8}$

Possible Answers:

a<b<c

a=b=c

a=c>b

a=c<b

Correct answer:

a=c>b

Explanation:

a) $\sqrt{64}$ = 8

b) percent of $= 64\cdot.10=6.4$

c) $\frac{64}{8}$ $=64\div8=8$

Therefore (a) and (c) are the same, and they are both larger than (b).

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Example Question #2 : How To Make Non Geometric Comparisons

Examine (a), (b), and (c) and choose the best answer.

a) percent of percent of 400

b) 400 percent of percent of

c) percent of 400 percent of

Possible Answers:

a=b=c

c>a>b

a>b>c

a<b<c

Correct answer:

a=b=c

Explanation:

a) percent of percent of 400

$.85\cdot.15\cdot400=51$

b) 400 percent of percent of

$4.00\cdot.85\cdot15=51$

c) percent of 400 percent of

$.15\cdot4.00\cdot85=51$

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

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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 #41 : How To Make Geometric Comparisons

Example Question #1 : How To Make Non Geometric Comparisons

Example Question #1 : Non Geometric Comparison

Example Question #2 : Non Geometric Comparison

Example Question #1 : Non Geometric Comparison

Example Question #1 : How To Make Non Geometric Comparisons

Example Question #2 : How To Make Non Geometric Comparisons

Example Question #1 : How To Make Non Geometric Comparisons

Example Question #8 : Non Geometric Comparison

Example Question #2 : How To Make Non Geometric Comparisons

All HSPT Quantitative Resources

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