GMAT Math : Geometry

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Example Questions

Example Question #1 : Midpoint Formula

Find the midpoint of segment $\displaystyle PS$ given that point $\displaystyle P$ is at (4,6) $\displaystyle (4,6)$.

I) The $\displaystyle x$ coordinate of $\displaystyle S$ is twice that of $\displaystyle P$, and the $\displaystyle y$ coordinate of $\displaystyle S$ is $\frac{3}{4}^{th}$ $\displaystyle \frac{3}{4}^{th}$ that of $\displaystyle P$.

II) $\displaystyle PS$ is $2\sqrt{5}$ $\displaystyle 2\sqrt{5}$ units long.

Possible Answers:

Both statements together are needed to answer the question.

Statement I is sufficient to answer the question, but Statement II is not sufficient to answer the question.

Either statement alone is sufficient to answer the question.

Neither statement is sufficient to answer the question. More information is needed.

Statement II is sufficient to answer the question, but Statement I is not sufficient to answer the question.

Correct answer:

Statement I is sufficient to answer the question, but Statement II is not sufficient to answer the question.

Explanation:

To find the midpoint, we need to know both endpoints.

I) Gives us the means to find out other endpoint.

II) Gives us the length of PS, but we are not given any hint as to its orientation.Thus, we cannot find the other endpoint and we cannot find the midpoint.

Thus, Statement I alone is sufficient to answer the question.

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Example Question #2901 : Gmat Quantitative Reasoning

Find the midpoint of segment $\displaystyle UI$.

I) Endpoint $\displaystyle I$ has coordinates of $\displaystyle (76,148)$.

II) Endpoint U's $\displaystyle U's$ $\displaystyle x$ coordinate is half of I's $\displaystyle I's$, and U's $\displaystyle U's$ $\displaystyle y$ coordinate is one sixteenth of I's $\displaystyle I's$ $\displaystyle y$ coordinate.

Possible Answers:

Both statements are needed to answer the question.

Neither statement is sufficient to answer the question. More information is needed.

Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.

Either statement is sufficient to answer the question.

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.

Correct answer:

Both statements are needed to answer the question.

Explanation:

To find the midpoint of a segment we need both endpoints

I) Gives us one endpoint.

II) Gives us clues to find the other endpoint.

$\displaystyle U$ has coordinates of $\displaystyle (38,9.25)$

Use midpoint formula

$(x_m,y_m)=\left(\frac{x_1-x_2}{2},\frac{y_1-y_2}{2}\right)$ $\displaystyle (x_m,y_m)=\left(\frac{x_1-x_2}{2},\frac{y_1-y_2}{2}\right)$

$(x_m,y_m)=\left(\frac{76-38}{2},\frac{148-9.25}{2}\right)=(19,69.375)$ $\displaystyle (x_m,y_m)=\left(\frac{76-38}{2},\frac{148-9.25}{2}\right)=(19,69.375)$

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GMAT Math : Geometry

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Midpoint Formula

Example Question #2901 : Gmat Quantitative Reasoning

All GMAT Math Resources

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