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} 15

\dpi{100} 12

\dpi{100} 30

\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

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

(C) \dpi{100} \frac{3}{4}

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)

(C) is greater than (A) and less 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}.

Example Question #1 : How To Make Non Geometric Comparisons

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

a) the square root of \displaystyle 121

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

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

Possible Answers:

\displaystyle a=b=c

\displaystyle a>b=c

\displaystyle a< b< c

\displaystyle a>b>c

Correct answer:

\displaystyle a>b=c

Explanation:

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

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

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

 

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

Example Question #3 : 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 \displaystyle 120

c) \displaystyle 60 percent of \displaystyle 110

Possible Answers:

\displaystyle a< b< c

\displaystyle b< a< c

\displaystyle a=b< c

\displaystyle a=b=c

Correct answer:

\displaystyle b< a< c

Explanation:

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

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

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

 

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

Example Question #4 : Non Geometric Comparison

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

a)  \displaystyle 2^{(2+3)}

b) \displaystyle 2(2+3)

c) \displaystyle \frac{2}{(2+3)}

 

 
Possible Answers:

\displaystyle a< b=c

\displaystyle a=b=c

\displaystyle a>b>c

\displaystyle a< b< c

Correct answer:

\displaystyle a>b>c

Explanation:

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

 

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

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

 

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

 

Example Question #5 : Non Geometric Comparison

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

a) \displaystyle 4^{2}

b) \displaystyle 2^{4}

c) \displaystyle 2^{2} + 4

Possible Answers:

\displaystyle a=b=c

\displaystyle a< b< c

\displaystyle a>b>c

\displaystyle a=b>c

Correct answer:

\displaystyle a=b>c

Explanation:

a) \displaystyle 4^{2} = 4\cdot 4 =16

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

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

 

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

Example Question #6 : Non Geometric Comparison

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

a)  \displaystyle 5+\frac{6+8}{2}

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

c)  \displaystyle \frac{5}{2}\cdot6+8

Possible Answers:

\displaystyle b>c>a

\displaystyle a=b=c

\displaystyle a=b>c

\displaystyle a>b>c

Correct answer:

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

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

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

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

Example Question #1 : Non Geometric Comparison

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

a) \displaystyle \sqrt{64}

b) \displaystyle 10 percent of \displaystyle 64

c) \displaystyle \frac{64}{8}

Possible Answers:

\displaystyle a=c< b

\displaystyle a< b< c

\displaystyle a=c>b

\displaystyle a=b=c

Correct answer:

\displaystyle a=c>b

Explanation:

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

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

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

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

Example Question #1 : How To Make Non Geometric Comparisons

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

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

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

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

Possible Answers:

\displaystyle c>a>b

\displaystyle a>b>c

\displaystyle a=b=c

\displaystyle a< b< c

Correct answer:

\displaystyle a=b=c

Explanation:

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

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

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

\displaystyle 4.00\cdot.85\cdot15=51

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

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

 

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

Example Question #1 : Non Geometric Comparison

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

a) \displaystyle 42 percent of \displaystyle 500

b) \displaystyle 21 percent of \displaystyle 1000

c) \displaystyle 84 percent of \displaystyle 250

Possible Answers:

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

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

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

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

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 \displaystyle 500

\displaystyle 500\cdot.42=210

b) \displaystyle 21 percent of \displaystyle 1000

\displaystyle 1000\cdot.21=210

c) \displaystyle 84 percent of \displaystyle 250

\displaystyle 250\cdot.84=210

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