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 #21 : How To Manipulate Numbers
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 #22 : Number Manipulation*
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 #23 : Number Manipulation*
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 #24 : 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 #29 : How To Manipulate Numbers
What number added to makes of ?
of is , because . Then, subtract to find the answer: