PSAT Math : Number Lines and Absolute Value
Study concepts, example questions & explanations for PSAT Math
All PSAT Math Resources
Example Questions
Example Question #52 : Integers
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 
The wrong answer is simplified in this manner:
And you can stop right here, for you know you will never have 
The other option is simplified in this manner:
This is just what you need!
Example Question #3 : Number Line
Which of the following is a graph for the values of 
Begin by solving for 
Now, this is represented by drawing an open circle at 6 and graphing upward to infinity:
Example Question #1 : Number Line
If the tick marks are equally spaced on the number line above, what is the average (arithmetic mean) of x, y, and z?
4
6
5
7
8
6
First, we must find out by how much they are spaced by. It cannot be 1, since 4(4) = 16, which is too great of a step in the positive direction and exceeds the equal-spacing limit. 2 works perfectly, however, as 4(2) equals 8 and fits in line with the equal spacing.
Next, we can find the values of x and y since we are given a value of 6 for the third tick mark. As such, x (6 – 4) and y (6 – 2) are 2 and 4, respectively.
Finally, z is 4 steps away from y, and since each step has a value of 2, 2(4) = 8, plus the value that y is already at, 8 + 4 = 12 (or can simply count).
Finding the average of all 3 values, we get (2 + 4 + 12)/3 = 18/3 = 6.
Example Question #11 : Number Lines And Absolute Value
How many numbers 1 to 250 inclusive are cubes of integers?
The cubes of integers from 1 to 250 are 1, 8, 27,64,125,216.
Example Question #3 : How To Find Value With A Number Line
Refer to the above number line. Which of the points is most likely the location of the number 
Therefore,
On the number line, 
Certified Tutor
All PSAT Math Resources
