GMAT Math : GMAT Quantitative Reasoning

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Example Questions

Example Question #21 : Lines

Thingy

In the above figure, give the union of $\overrightarrow{GE}$ and $\overrightarrow{OE}$ .

Possible Answers:

$\overrightarrow{OE}$

$\overrightarrow{GE}$

$\overline{OE}$

$\overline{GO}$

$\overleftrightarrow{GE}$

Correct answer:

$\overrightarrow{GE}$

Explanation:

$\overrightarrow{OE}$ can be seen to be completely contained in $\overrightarrow{GE}$ - that is, $\overrightarrow{OE}\subseteq \overrightarrow{GE}$ . The union of a set and its subset is the containing set, so the correct response is $\overrightarrow{GE}$ .

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Example Question #411 : Geometry

Thingy

Give the union of $\overrightarrow{NO}$ and $\overrightarrow{XO}$ in the above figure.

Possible Answers:

$\overline{XO}$

$\overline{NX}$

$\overrightarrow{NO}$

$\overleftrightarrow{NX}$

$\overrightarrow{XO}$

Correct answer:

$\overleftrightarrow{NX}$

Explanation:

The diagram below shows $\overrightarrow{NO}$ and $\overrightarrow{XO}$ 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 $\overleftrightarrow{NX}$ .

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Example Question #653 : Problem Solving Questions

Thingy

In the above figure, let be the midpoint of $\overline{EO}$ . Which of the following would give another name for $\overrightarrow{GM}$ ?

Possible Answers:

$\overrightarrow{OE}$

$\overrightarrow{ME}$

$\overrightarrow{EM}$

$\overrightarrow{GE}$

$\overrightarrow{MG}$

Correct answer:

$\overrightarrow{GE}$

Explanation:

Below is the diagram with midpoint of $\overline{EO}$ added; also, $\overrightarrow{GM}$ , 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. $\overrightarrow{GM}$ has as an endpoint, and also includes the points and , so there are two valid alternative names, $\overrightarrow{GE}$ and $\overrightarrow{GO}$ , among the choices. The correct response is $\overrightarrow{GE}$ .

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Example Question #11 : Understanding Rays

Thingy

In the above diagram, let and be the midpoints of $\overline{OG}$ and $\overline{OE}$ , respectively, and and be the midpoints of $\overline{GK}$ and $\overline{OL}$ , respectively. Which of the following is not a valid alternative name for $\overrightarrow{RS}$ ?

Possible Answers:

Each of the other choices gives a valid alternative name for $\overrightarrow{RS}$ .

$\overrightarrow{RL}$

$\overrightarrow{RE}$

$\overrightarrow{RK}$

$\overrightarrow{RO}$

Correct answer:

Each of the other choices gives a valid alternative name for $\overrightarrow{RS}$ .

Explanation:

Below is the diagram with the points K,L,R , and , as described, shown in green. Also, $\overrightarrow{RS}$ , the ray that has endpoint and passes through , is marked in red.

Thingy_x

The ray also passes through E,K,L, and , so $\overrightarrow{RE}$ , $\overrightarrow{RK}$ , $\overrightarrow{RL}$ , and $\overrightarrow{RO}$ —all four given names—are also valid names for the ray.

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Example Question #1 : Calculating An Angle Of A Line

What is the measure of an angle complementary to a $72 ^{\circ }$ angle?

Possible Answers:

$162 ^{\circ }$

$18 ^{\circ }$

$108 ^{\circ }$

$72 ^{\circ }$

$36 ^{\circ }$

Correct answer:

$18 ^{\circ }$

Explanation:

Complementary angles have degree measures that total $90 ^{\circ }$ , so the measure of an angle complementary to a $72 ^{\circ }$ angle would have measure $(90-72)^{\circ } = 18 ^{\circ }$ .

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Example Question #1 : Calculating An Angle Of A Line

What is the measure of an angle congruent to a $48 ^{\circ }$ angle?

Possible Answers:

$48 ^{\circ }$

$42 ^{\circ }$

$24 ^{\circ }$

$138^{\circ }$

$132 ^{\circ }$

Correct answer:

$48 ^{\circ }$

Explanation:

Two angles are congruent if they have the same degree measure, so an angle will be congruent to a $48 ^{\circ }$ angle if its measure is also $48 ^{\circ }$ .

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Example Question #411 : Geometry

What is the measure of an angle supplementary to a $66 ^{\circ }$ angle?

Possible Answers:

$33 ^{\circ }$

$24 ^{\circ }$

$156 ^{\circ }$

$66 ^{\circ }$

$114 ^{\circ }$

Correct answer:

$114 ^{\circ }$

Explanation:

Supplementary angles have degree measures that total $180 ^{\circ }$ , so the measure of an angle complementary to a $66 ^{\circ }$ angle would have measure $\left ( 180- 66 \right )^{\circ } = 114^{\circ }$ .

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Example Question #2 : Calculating An Angle Of A Line

What is the measure of an angle that is supplementary to a $68^{\circ}$ angle?

Possible Answers:

$68^{\circ}$

$112^{\circ}$

$22^{\circ}$

$292^{\circ}$

$86^{\circ}$

Correct answer:

$112^{\circ}$

Explanation:

Supplementary angles have degree measures that total $180^{\circ}$ , so an angle supplementary to $68^{\circ}$ would measure $180^{\circ}-68^{\circ}=112^{\circ}$ .

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Example Question #2 : Calculating An Angle Of A Line

What is the measure of an angle congruent to a $58^{\circ}$ angle?

Possible Answers:

$302^{\circ}$

$122^{\circ}$

$90^{\circ}$

$58^{\circ}$

$32^{\circ}$

Correct answer:

$58^{\circ}$

Explanation:

Congruent angles have degree measures that are equal, so an angle congruent to $58^{\circ}$ is $58^{\circ}$ .

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Example Question #422 : Geometry

What is the measure of an angle that is complementary to a $42^{\circ }$ angle?

Possible Answers:

$90^{\circ }$

$24^{\circ }$

$48^{\circ }$

$318^{\circ }$

$138^{\circ }$

Correct answer:

$48^{\circ }$

Explanation:

Complementary angles have degree measures that total $90^{\circ}$ , so an angle complementary to $42^{\circ}$ would measure $90^{\circ}-42^{\circ}=48^{\circ}$ .

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GMAT Math : GMAT Quantitative Reasoning

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #21 : Lines

Example Question #411 : Geometry

Example Question #653 : Problem Solving Questions

Example Question #11 : Understanding Rays

Example Question #1 : Calculating An Angle Of A Line

Example Question #1 : Calculating An Angle Of A Line

Example Question #411 : Geometry

Example Question #2 : Calculating An Angle Of A Line

Example Question #2 : Calculating An Angle Of A Line

Example Question #422 : Geometry

All GMAT Math Resources

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