All HSPT Quantitative Resources
Example Questions
Example Question #21 : Number Manipulation*
What is the difference between and
?
First, square the numbers:
Then, subtract to find the difference:
Example Question #22 : Number Manipulation*
What is the average of ,
, and
?
First, .
Then, find the sum and divide by the number of elements:
Example Question #23 : How To Manipulate Numbers
is
percent of what number divided by
?
First, find the number that is
percent of. We will call that unknown number
:
Then, multiply by three to reverse the division:
Example Question #24 : How To Manipulate Numbers
is what percent of
?
Using to represent the unknown percentage, we can say that
.
Divide both sides by to find
:
Rewritten as a percent, is
percent.
Example Question #25 : How To Manipulate Numbers
What is the ratio of the circumference of a circle with a radius of to the circumference of a circle with a radius of
?
The formula for circumference is .
For the first circle:
And for the second:
The ratio is then , or
.
Example Question #26 : How To Manipulate Numbers
What is percent of the product of
and
?
Work backwards to solve this problem. First, the product of and
is:
Second, percent of that is:
Example Question #27 : How To Manipulate Numbers
What number is more than
of
?
First, of
is
, because
.
Then, add :
Example Question #28 : How To Manipulate Numbers
What number divided by equals
of
?
First, of
is
because
.
Then, multiply by to reverse the division:
Example Question #23 : Number Manipulation*
What number is twice as much as the square root of ?
The square root of is
because
. Next, multiply by
to find twice as much:
Example Question #30 : How To Manipulate Numbers
What number added to makes
of
?
of
is
, because
. Then, subtract
to find the answer:
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All HSPT Quantitative Resources
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