HSPT Quantitative : How to make non-geometric comparisons
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Example Questions
Example Question #51 : Non Geometric Comparison
Examine (a), (b), and (c) to find the best answer:
a) 
b) 
c) 
(a) is two times greater than (c)
(a) is two times greater than (b)
(a) is four times greater than (b)
(a) is four times greater than (c)
(a) is four times greater than (c)
Calculate each expression to compare the values:
a) 
b) 
c) 
(a) and (b) are equal, and (a) is four times greater than (c) because:
Example Question #51 : How To Make Non Geometric Comparisons
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
(a) equals (b) but not (c)
(a), (b), and (c) are all unequal
(a), (b), and (c) are all equal
(a) equals (c) but not (b)
(a), (b), and (c) are all unequal
In (b), the expressions are multiplied. Both the coefficents and variables are multiplied together:
In (b), the terms are added together. Since they are like terms, the coefficients simply add together:
Now that everything is simplified, we can tell that they are all unequal.
Example Question #53 : Non Geometric Comparison
Examine (a), (b), and (c) to find the best answer:
a) 
b) 
c) 
Calculate each expression to compare the values:
a) 
b) 
c) 
It is now evident that (a) is smaller than (b), which is smaller than (c).
Example Question #52 : How To Make Non Geometric Comparisons
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
(a), (b), and (c) are all equal
(a) is equal to (b) but not (c)
(a), (b), and (c) are all unequal
(a) is equal to (c) but not (b)
(a) is equal to (b) but not (c)
When two elements are multiplied inside of a square root, it is the same as if each of their square roots were multiplied together. Therefore (a) simplifies like this:
This is equal to (b), but not (c)
Example Question #53 : How To Make Non Geometric Comparisons
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
(a), (b) and (c) are all equal
(a) is equal to (b) but not (c)
(a), (b) and (c) are all unequal
(a) is equal to (c) but not (b)
(a) is equal to (b) but not (c)
Simplify each expression to compare them. Remember for (c) that an exponent outside of parentheses distributes to each of the elements inside:
a)
b) 
c) 
(a) is equal to (b) but not (c)
Example Question #54 : How To Make Non Geometric Comparisons
Examine (a), (b), and (c) to find the best answer:
a)
b) 
c)
Convert each value to a decimal to compare them:
a) 
b) 
c) 
It is now evident that (a) is bigger than (b) which is bigger than (c).
Example Question #55 : How To Make Non Geometric Comparisons
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
(a) is equal to (c) but not (b)
(a), (b), and (c) are all unequal
(a), (b), and (c) are all equal
(a) is equal to (b) but not (c)
(a) is equal to (c) but not (b)
When doing these calculation, be sure to follow the order of operations and do the multiplication before the addition:
a)
b)
c)
(a) and (c) are both 
Example Question #56 : How To Make Non Geometric Comparisons
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
Choose a common denominator to compare the fractions. One choice is 
a)
b)
c)
It is now clear that (b) is smaller than (a), which is smaller than (c)
Example Question #57 : How To Make Non Geometric Comparisons
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
(a) equals (c) but not (b)
(a) equals (b) but not (c)
(a), (b), and (c) are all unequal
(a), (b), and (c) are all equal
(a), (b), and (c) are all equal
Both 
Since each of these portions are multiplied by 
Example Question #58 : How To Make Non Geometric Comparisons
Examine (a), (b), and (c) to find the best answer:
a) half of
b) double
c) quarter of
Multiply each fraction by the proportion described in words:
a) half of
b) double
c) quarter of
With a common denominator, you can compare the fractions and see that (a) is smaller than (c), which is smaller than (b).
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