Questions that involve number lines overwhelmingly ask for information about the position of a point or points or the distance between two points.
On any number line you will see, numbers get bigger as they move from left to right. For example:
| B is greater than A. | B is more positive than A (if both positive). |
| A is less than B. | A is more negative than B (if both negative). |
The statements shown are true regardless of where 0 is on the number line. Points A and B could both be positive or both be negative, or A could be negative and B could be positive.
Number lines on the GRE follow rules similar to the rules for geometric shapes. If there is more than one point on a number line, you KNOW the Relative Position of each point.
While you do know the relative position of each point, you do not know the Relative Distance between points (unless that information is specifically provided).
On the preceding number line, B could be closer to A than to C, closer to C than to A, or equidistant between A and C. Without more information, there is no way to know.
The rules are similar if a number line contains both numbers and variables. For example:
Point D looks like it is halfway between 1 and 2, but that does not mean that it is 1.5. Point D could be 1.5, but it could also be 1.000001, or 1.99999 or, in fact, any number between 1 and 2.
Refer to the following number line for questions #1–3.
Which of the following MUST be true?
v > s + t
v + s > t + r
rs > v
If you know the specific location of two points on a number line, the distance between them is the absolute value of their difference. For example:
If a number line contains tick marks and specifically tells you they are evenly spaced, it may be necessary to calculate the distance between tick marks.
On an evenly spaced number line, tick marks represent specific values, and the intervals between tick marks represent the distance between tick marks.
For any specific range, there will always be one more tick mark than interval, for example:
On this number line, there are four tick marks between 2 and 5 (inclusive). There is one fewer interval than tick marks. There are only three intervals between 2 and 5. Now calculate the length of the intervals on this number line. To calculate the distance between any two tick marks (which is the same as the length of the intervals), subtract the lower bound from the upper bound and divide the difference by the number of intervals.
In the previous number line, the lower bound is 2, the upper bound is 5, and there are three intervals between 2 and 5. Use these numbers to calculate the distance between tick marks on the number line:
That means that each tick mark in the preceding number line is 1 unit away from each of the two tick marks to which it is adjacent.
Not every number line will have interval lengths with integer values. Note that this method is equally effective if the intervals are fractional amounts. What is the distance between adjacent tick marks on the following number line?
Now the range contains six tick marks and five intervals.
Thus, the distance between tick marks is
:
On the number line above, what is the value of point x?