HSPT Quantitative : How to make non-geometric comparisons

Study concepts, example questions & explanations for HSPT Quantitative

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Example Questions

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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} 30

\dpi{100} 24

\dpi{100} 12

\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

Example Question #2 : 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

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

Possible Answers:

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

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

Example Question #3 : How To Make Non Geometric Comparisons

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

a) the square root of 

b)  of 

c) the average of  & 

Possible Answers:

Correct answer:

Explanation:

a) The square root of  is , because .

b)  of  is , because .

c) The average of  and  is , because .

 

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

Example Question #4 : How To Make Non Geometric Comparisons

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

a)  percent of 

b)  percent of 

c)  percent of 

Possible Answers:

Correct answer:

Explanation:

a)  percent of  is  because .

b)  percent of  is  because .

c)  percent of  is  because .

 

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

Example Question #5 : How To Make Non Geometric Comparisons

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

a)  

b) 

c) 

 

 
Possible Answers:

Correct answer:

Explanation:

a)   

 

b)  

c)  

 

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

 

Example Question #6 : How To Make Non Geometric Comparisons

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

a) 

b) 

c) 

Possible Answers:

Correct answer:

Explanation:

a) 

b)

c) 

 

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

Example Question #1 : How To Make Non Geometric Comparisons

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

a)  

b)

c)  

Possible Answers:

Correct answer:

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) 

b)  

c)  

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

Example Question #2 : How To Make Non Geometric Comparisons

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

a) 

b)  percent of 

c) 

Possible Answers:

Correct answer:

Explanation:

a)  

b)  percent of  

c) 

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

Example Question #8 : How To Make Non Geometric Comparisons

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

a)  percent of  percent of 

b)  percent of  percent of 

c)  percent of  percent of 

Possible Answers:

Correct answer:

Explanation:

a)  percent of  percent of 

b)  percent of  percent of 

c)  percent of  percent of 

 

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

Example Question #10 : Non Geometric Comparison

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

a)  percent of 

b)  percent of 

c)  percent of 

Possible Answers:

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

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

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

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

b)  percent of 

c)  percent of 

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