### All GMAT Math Resources

## Example Questions

### Example Question #11 : Understanding Rays

In the above figure, give the union of and .

**Possible Answers:**

**Correct answer:**

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 #12 : Understanding Rays

Give the union of and in the above figure.

**Possible Answers:**

**Correct answer:**

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 #13 : Understanding Rays

In the above figure, let be the midpoint of . Which of the following would give another name for ?

**Possible Answers:**

**Correct answer:**

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 #14 : Understanding Rays

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 ?

**Possible Answers:**

Each of the other choices gives a valid alternative name for .

**Correct answer:**

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.