HSPT Quantitative : Non-Geometric Comparison
Study concepts, example questions & explanations for HSPT Quantitative
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Example Questions
Example Question #71 : Non Geometric Comparison
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
(a), (b), and (c) are all equal
(b) is equal to (c) but not (a)
(b) is equal to (a) but not (c)
(a), (b), and (c) are all unequal
(b) is equal to (c) but not (a)
The property of exponents to remember here is that 
This explains why (b) and (c) are equal. (a) cannot be equal because 
Example Question #72 : Non Geometric Comparison
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
(a) is equal to (c) but not (b)
(a) is equal to (b) but not (c)
(a), (b), and (c) are all unequal
(a), (b), and (c) are all equal
(a) is equal to (c) but not (b)
Following the order of operations, (a) simplifies to be (c):
(b) simplifies to the following:
Example Question #73 : Non Geometric Comparison
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
Find a common denominator to compare the fractions. Here, we use 
a)
b)
c)
It is now evident that (a) is greater than (b), which is greater than (c).
Example Question #74 : Non Geometric Comparison
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 equal
(a), (b), and (c) are all unequal
(a) equals (c) but not (b)
(a), (b), and (c) are all equal
(a) is a simplified version of both (b) and (c). For (b), you can add the like terms together and end up with (a). For (c), you can multiply the constants and the variables together and also end up with (a). To test this, try substituting a number in for 
Example Question #75 : Non Geometric Comparison
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
(a), (b), and (c) are all equal
(a), (b), and (c) are all unequal
(a) is equal to (b) but not (c)
(a) is equal to (c) but not (b)
(a) is equal to (b) but not (c)
Test this problem by substituting a number in for 
a)
b)
c)
It is evident that (a) and (b) are equal but (c) is not.
Example Question #76 : Non Geometric Comparison
Examine (a), (b), and (c) to find the best answer:
a) 
b)
c)
Convert all of the values into decimals to compare them:
a) 
b)
c)
It is now evident that (a) is smaller than (c), which is smaller than (b)
Example Question #77 : Non Geometric Comparison
Examine (a), (b), and (c) to find the best answer:
a) 
b)
c)
(a), (b), and (c) are all unequal
(a) is equal to (b) but not (c)
(a) is equal to (c) but not (b)
(a), (b), and (c) are all equal
(a) is equal to (b) but not (c)
To find the percent of a number, in this case 
Therefore, (a) and (b) are equal. 
Example Question #78 : Non Geometric Comparison
Examine (a), (b), and (c) to find the best answer:
a) 
b)
c)
(a), (b), and (c) are all equal
(a) is equal to (c) but not (b)
(a) is equal to (b) but not (c)
(a), (b), and (c) are all unequal
(a) is equal to (c) but not (b)
To find a percentage of the number, multiply it by the decimal version of the percent, or the percent divided by 
Therefore, 
Example Question #79 : Non Geometric Comparison
Exmaine (a), (b), and (c) to find the best answer:
a) 
b) 
c) 
Multiply out each expression to compare the values:
a)
b)
c)
It is now evident that (a) is smaller than (c), which is smaller than (b)
Example Question #80 : Non Geometric Comparison
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
(a), (b) and (c) are all equal
(a), (b) and (c) are all unequal
(a) is equal to (c) but not (b)
(a) is equal to (b) but not (c)
(a), (b) and (c) are all equal
You don't need to calculate any square roots to solve this problem! Just remember the following property:
Following this property, (a) and (b) are equal:
This also means that the following is true:
And therefore:
(c) is just a simplified version of (a) and (b)
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