HSPT Quantitative : How to make non-geometric comparisons
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Example Questions
Example Question #61 : 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 unequal
(a) equals (c) but not (b)
(a), (b), and (c) are all equal
(a) equals (c) but not (b)
To compare the expressions, distribute and simplify:
a) 
b) 
c)
It is now clear that (a) and (c) are equal but (b) is not.
Example Question #62 : 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), (b), and (c) are all equal
(a) is equal to (c) but not (b)
(a), (b), and (c) are all equal
The important property of square roots to remember here is that
This means that (a) can be broken up into the following:
These variations are all equal
Example Question #63 : How To Make Non Geometric Comparisons
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
(a) 
Example Question #63 : Non Geometric Comparison
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
(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)
(a), (b), and (c) are all unequal
One way to test this answer is to substitute in numbers for the variables. For example, let's say that 
a)
b)
c)
None are equal!
Example Question #64 : Non Geometric Comparison
Examine (a), (b), and (c) to find the best answer:
a) 
b) 
c) 
Multiply the fractions by the integers in order to compare the expressions:
a)
b)
c)
It is now clear that (b) is smaller than (a), which is smaller than (c).
Example Question #64 : Non Geometric Comparison
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
(a) equals (c) and is greater than (b)
(a) equals (c) and is less than (b)
(a), (b), and (c) are all equal
(a), (b), and (c) are all unequal
(a) equals (c) and is greater than (b)
The property of exponents to remember here is that 
This means that 
Example Question #66 : Non Geometric Comparison
Examine (a), (b), and (c) to find the best answer:
(a)
(b)
(c) 
Converted into decimals, the numbers look like this:
a)
b)
c) 
It is now evident that (c) is smaller than (a), which is smaller than (b)
Example Question #65 : Non Geometric Comparison
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
(a), (b), and (c) are all equal
(a) equals (c) but not (b)
(a), (b), and (c) are all unequal
(a) equals (b) but not (c)
(a) equals (b) but not (c)
Try substituting a number in for 
a)
b)
c)
It is now evident that (a) and (b) are equal, but not (c)
Example Question #66 : Non Geometric Comparison
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
(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)
(a) is equal to (b) but not (c)
(b) is a factored version of (a). (c), however, is not raised to the same exponent. Test this by plugging a number in for 
a)
b)
c)
(a) and (b) are equal, but (c) is not.
Example Question #67 : Non Geometric Comparison
Examine (a), (b), and (c) to find the best answer:
a) 
b)
c)
Convert each to a decimal in order to compare them:
a)
b)
c)
It is now evident that (a) is smaller than (c), which is smaller than (b).
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