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HSPT Quantitative : Non-Geometric Comparison

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Example Questions

Example Question #1 : Non Geometric Comparison

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

Possible Answers:

$\dpi{100} 12$ $\displaystyle \dpi{100} 12$

$\dpi{100} 24$ $\displaystyle \dpi{100} 24$

$\dpi{100} 30$ $\displaystyle \dpi{100} 30$

$\dpi{100} 15$ $\displaystyle \dpi{100} 15$

Correct answer:

$\dpi{100} 24$ $\displaystyle \dpi{100} 24$

Explanation:

Set up the following equation.

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

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

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

$\dpi{100} x=24$ $\displaystyle \dpi{100} x=24$

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Example Question #1 : How To Make Non Geometric Comparisons

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

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

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

Possible Answers:

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

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

(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.

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

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

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Example Question #1 : Non Geometric Comparison

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

a) the square root of 121 $\displaystyle 121$

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

c) the average of $\displaystyle 5$ & $\displaystyle 15$

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:

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

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

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

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

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Example Question #2 : Non Geometric Comparison

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

a) $\displaystyle 50$ percent of $\displaystyle 96$

b) $\displaystyle 30$ percent of 120 $\displaystyle 120$

c) $\displaystyle 60$ percent of 110 $\displaystyle 110$

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

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

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

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

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

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Example Question #1 : Non Geometric Comparison

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

a) ^{$\displaystyle 2^{(2+3)}$}

b) 2(2+3) $\displaystyle 2(2+3)$

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

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:

a) ^{$\displaystyle 2^{(2+3)}$ $\displaystyle = 2^{5} = 2\cdot 2\cdot 2\cdot 2\cdot 2 = 32$}

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

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

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

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Example Question #1 : Non Geometric Comparison

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

a) $4^{2}$ $\displaystyle 4^{2}$

b) $2^{4}$ $\displaystyle 2^{4}$

c) $2^{2} + 4$ $\displaystyle 2^{2} + 4$

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:

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

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

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

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

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Example Question #2 : Non Geometric Comparison

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

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

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

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

Possible Answers:

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

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

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

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

Correct answer:

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

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

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

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

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

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Example Question #2 : How To Make Non Geometric Comparisons

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

a) $\sqrt{64}$ $\displaystyle \sqrt{64}$

b) $\displaystyle 10$ percent of $\displaystyle 64$

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

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:

a) $\sqrt{64}$ $\displaystyle \sqrt{64}$ = 8 $\displaystyle = 8$

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

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

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

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Example Question #3 : Non Geometric Comparison

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

a) $\displaystyle 85$ percent of $\displaystyle 15$ percent of 400 $\displaystyle 400$

b) 400 $\displaystyle 400$ percent of $\displaystyle 85$ percent of $\displaystyle 15$

c) $\displaystyle 15$ percent of 400 $\displaystyle 400$ percent of $\displaystyle 85$

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

a) $\displaystyle 85$ percent of $\displaystyle 15$ percent of 400 $\displaystyle 400$

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

b) 400 $\displaystyle 400$ percent of $\displaystyle 85$ percent of $\displaystyle 15$

$4.00\cdot.85\cdot15=51$ $\displaystyle 4.00\cdot.85\cdot15=51$

c) $\displaystyle 15$ percent of 400 $\displaystyle 400$ percent of $\displaystyle 85$

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

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

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Example Question #3 : Non Geometric Comparison

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

a) $\displaystyle 42$ percent of 500 $\displaystyle 500$

b) $\displaystyle 21$ percent of 1000 $\displaystyle 1000$

c) $\displaystyle 84$ percent of 250 $\displaystyle 250$

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) $\displaystyle 42$ percent of 500 $\displaystyle 500$

$500\cdot.42=210$ $\displaystyle 500\cdot.42=210$

b) $\displaystyle 21$ percent of 1000 $\displaystyle 1000$

$1000\cdot.21=210$ $\displaystyle 1000\cdot.21=210$

c) $\displaystyle 84$ percent of 250 $\displaystyle 250$

$250\cdot.84=210$ $\displaystyle 250\cdot.84=210$

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HSPT Quantitative : Non-Geometric Comparison

Study concepts, example questions & explanations for HSPT Quantitative

All HSPT Quantitative Resources

Example Questions

Example Question #1 : Non Geometric Comparison

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 : Non Geometric Comparison

Example Question #2 : Non Geometric Comparison

Example Question #2 : How To Make Non Geometric Comparisons

Example Question #3 : Non Geometric Comparison

Example Question #3 : Non Geometric Comparison

All HSPT Quantitative Resources

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