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HSPT Quantitative : How to make non-geometric comparisons

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

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Example Question #42 :Hspt Quantitative Skills

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

Possible Answers:

$\dpi{100} 15$

$\dpi{100} 30$

$\dpi{100} 12$

$\dpi{100} 24$

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 :How To Make Non Geometric Comparisons

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

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

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

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 #44 :Hspt Quantitative Skills

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 ofandis, 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 :How To Make Non Geometric Comparisons

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

a=b<c

b<a<c

Correct answer:

b<a<c

Explanation:

a)percent ofisbecause $96\cdot .50=48$ .

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

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

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

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Example Question #46 :Hspt Quantitative Skills

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 #48 :Hspt Quantitative Skills

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 #49 :Hspt Quantitative Skills

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

a) $\sqrt{64}$

b)percent of

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

Possible Answers:

a=c<b

a=c>b

a<b<c

a=b=c

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 #50 :Hspt Quantitative Skills

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

a)percent ofpercent of 400

b) 400 percent ofpercent 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 ofpercent of 400

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

b) 400 percent ofpercent 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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Example Question #2 :How To Make Non Geometric Comparisons

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

a)percent of 500

b)percent of 1000

c)percent of 250

Possible Answers:

(b) is greater than (a) or (c)

(b) is the greatest, and (a) and (c) are equal

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

Correct answer:

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

Explanation:

In each of these scenarios, if the percentage increases, the number decreases by the same factor. All cases are the same value:

a)percent of 500

$500\cdot.42=210$

b)percent of 1000

$1000\cdot.21=210$

c)percent of 250

$250\cdot.84=210$

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All HSPT Quantitative Resources

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HSPT Quantitative : How to make non-geometric comparisons

Study concepts, example questions & explanations for HSPT Quantitative

All HSPT Quantitative Resources

Example Questions

Example Question #42 :Hspt Quantitative Skills

Example Question #1 :How To Make Non Geometric Comparisons

Example Question #44 :Hspt Quantitative Skills

Example Question #1 :How To Make Non Geometric Comparisons

Example Question #46 :Hspt Quantitative Skills

Example Question #2 :How To Make Non Geometric Comparisons

Example Question #48 :Hspt Quantitative Skills

Example Question #49 :Hspt Quantitative Skills

Example Question #50 :Hspt Quantitative Skills

Example Question #2 :How To Make Non Geometric Comparisons

All HSPT Quantitative Resources

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