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HSPT Quantitative : How to make non-geometric comparisons

Study concepts, example questions & explanations for HSPT Quantitative

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Example Questions

Example Question #1 : Non Geometric Comparison

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

Possible Answers:

$\dpi{100} 12$

$\dpi{100} 24$

$\dpi{100} 30$

$\dpi{100} 15$

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)

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

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

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 #1 : 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 #2 : 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 : Non Geometric Comparison

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 #1 : Non Geometric Comparison

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 #2 : Non Geometric Comparison

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:

a=b>c

b>c>a

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 #2 : 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=c<b

a<b<c

a=c>b

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 #3 : Non Geometric Comparison

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

a=b=c

a>b>c

c>a>b

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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Example Question #3 : Non Geometric Comparison

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 #1 : Non Geometric Comparison

Example Question #1 : Non Geometric Comparison

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 : Non Geometric Comparison

Example Question #3 : Non Geometric Comparison

Example Question #3 : Non Geometric Comparison

All HSPT Quantitative Resources

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