GMAT Math : Understanding rays

Study concepts, example questions & explanations for GMAT Math

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Example Questions

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Example Question #11 : Understanding Rays

Thingy

In the above figure, give the union of  and .

Possible Answers:

Correct answer:

Explanation:

 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

Thingy

Give the union of  and  in the above figure.

Possible Answers:

Correct answer:

Explanation:

The diagram below shows  and  in red and green, respectively:

Thingy_x

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

Thingy

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

Possible Answers:

Correct answer:

Explanation:

Below is the diagram with midpoint  of  added; also, , the ray starting at  and passing through , is in green.

Thingy x

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

Thingy

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 .

Explanation:

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.

Thingy_x

The ray also passes through  and , so , and —all four given names—are also valid names for the ray. 

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