All GMAT Math Resources
Example Questions
Example Question #21 : Lines
In the above figure, give the union of and .
can be seen to be completely contained in - that is, . The union of a set and its subset is the containing set, so the correct response is .
Example Question #22 : Lines
Give the union of and in the above figure.
The diagram below shows and in red and green, respectively:
The union of the two sets is the set of points in one or the other; this set is the entire line containing the two rays, which is .
Example Question #653 : Problem Solving Questions
In the above figure, let be the midpoint of . Which of the following would give another name for ?
Below is the diagram with midpoint of added; also, , the ray starting at and passing through , is in green.
A ray is named after, in order, its endpoint and any other point on the ray. has as an endpoint, and also includes the points and , so there are two valid alternative names, and , among the choices. The correct response is .
Example Question #23 : Lines
In the above diagram, let and be the midpoints of and , respectively, and and be the midpoints of and , respectively. Which of the following is not a valid alternative name for ?
Each of the other choices gives a valid alternative name for .
Each of the other choices gives a valid alternative name for .
Below is the diagram with the points , and , as described, shown in green. Also, , the ray that has endpoint and passes through , is marked in red.
The ray also passes through and , so , , , and —all four given names—are also valid names for the ray.