All GRE Math Resources
Example Questions
Example Question #2 : How To Find Value With A Number Line
If perimeter of equilateral triangle is , what is the height of the triangle?
Since perimeter of equilateral triangle is and we have three equal sides, we just divide that vaue by to get . To find height, we can set-up a proportion.
The height is opposite the angle . Side opposite is and the side of equilateral triangle which is opposite is .
Cross multiply.
Divide both sides by
Let's simplify by factoring out to get a final answer of .
Example Question #692 : Arithmetic
On a real number line, x1 = -4 and x2 = 14. What is the distance between these two points?
-18
4
18
10
18
The distance between two points is always positive. We calculate lx2 - x1l, which will give us the distance between the points.
|14- (-4)| = |14+4| = |18| = 18
Example Question #1 : How To Graph An Inequality With A Number Line
Which of the following is a graph for the values of defined by the inequality stated above?
To begin, you must simplify so that you "isolate" , (i.e. at least eliminate any coefficients from it). To do this, divide all of the members of the inequality by :
Now, this inequality represents all of the numbers between 13 and 32. However, it does include (hence, getting a closed circle for that value) and does not include (hence, getting an open circle for that value). Therefore, it looks like:
Example Question #561 : Arithmetic
Which of the following inequalities is represented by the number line shown above?
Since the inequality represents one range of values between two end points (both of which are included, given the sign being "less than or equal"), you know that whatever you answer, it must be convertible to the form:
Now, you know that it is impossible to get this out of the choices that have no absolute values involved in them. Therefore, the only options that make sense are the two having absolute values; however, here you should choose only the ones that have a , for only that will yield a range like this. Thus, we can try both of our options.
The wrong answer is simplified in this manner:
And you can stop right here, for you know you will never have for the left terminus.
The other option is simplified in this manner:
This is just what you need!
Example Question #5 : Number Line
Quantity A:
Quantity B:
Quantity B is larger.
The two quantities are equal.
The relationship cannot be determined.
Quantity A is larger.
Quantity B is larger.
It is not necessary to solve this problem by multiplying terms out. Notice that between quantities A and B, the last three terms switch places for the two large numbers. as such they can be rewritten:
Quantity A:
Quantity B:
Both quantities A and B share the exact same terms, save for two:
Quantity A:
Quantity B:
From visual inspection, it is clear that B is larger.
Example Question #1 : How To Graph An Inequality With A Number Line
Which of the following is true?
Since is always positive, and , it follows that for all possible values.
For the A, it is possible to choose values that make the statement false, for example and .
C is always false.
Example Question #124 : Arithmetic
Which of the statements is always true?
Although C may approach zero for large values of and values of , it will never actually reach it for real values.
A and B, however, have x and y values which make them false:
For A, an example is
For B, would make the value zero.
Example Question #2 : How To Graph An Inequality With A Number Line
Which of the following is a graph for the values of defined by the inequality stated above?
Begin by solving for :
Now, this is represented by drawing an open circle at 6 and graphing upward to infinity:
Example Question #121 : Arithmetic
Quantity A:
Quantity B:
The relationship cannot be determined from the information given.
The two quantities are equal
Quantity A is greater
Quantity B is greater
Quantity A is greater
Since both quantities have an , you can ignore this variable, which will give you and for quantities A and B, respectively. Since and are both negative numbers, must be bigger than , which means that no matter what numbers they are, Quantity A must be bigger.
Example Question #122 : Arithmetic
If and are integers such that and , what is the smallest possible value of ?
To make as small as possible, let be as small as possible , and subtract the largest value of possible :