GMAT Math : Geometry

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Example Questions

Example Question #691 : Geometry

In the -plane, what is the slope of the line with equation $4x+5y=8$ ?

Possible Answers:

$4$

$\frac{8}{5}$

$\frac{1}{2}$

$-4$

$-\frac{4}{5}$

Correct answer:

$-\frac{4}{5}$

Explanation:

Put the equation in slope-intercept form to solve for the slope:

$y=mx+b$ , where m is the slope and b is the intercept

Rearrange terms: $5y=-4x+8$

Divide by 5: $y=-\frac{4}{5}x+\frac{8}{5}$

slope = $-\frac{4}{5}$

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Example Question #91 : Coordinate Geometry

Give the slope of the line with the equation $\frac{4}{3} x = \frac{2}{5} y - 10$ .

Possible Answers:

$\frac{3}{10}$

$\frac{10}{3}$

$\frac{1}{25}$

$\frac{8}{15}$

$\frac{15}{8}$

Correct answer:

$\frac{10}{3}$

Explanation:

Rewrite in slope-intercept form:

$\frac{4}{3} x = \frac{2}{5} y - 10$

$\frac{4}{3} x + 10 = \frac{2}{5} y - 10 + 10$

$\frac{2}{5} y = \frac{4}{3} x + 10$

$\frac{5} {2} \cdot \frac{2}{5} y= \frac{5} {2} \cdot \left ( \frac{4}{3} x + 10 \right )$

$y= \frac{5} {2} \cdot \frac{4}{3} x + \frac{5} {2} \cdot 10$

$y= \frac{10}{3} x +25$

The slope is the coefficient of , which is $\frac{10}{3}$ .

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Example Question #92 : Coordinate Geometry

Fill in the circle with a number so that the graph of the resulting equation has slope $\frac{4}{5}$ :

$\bigcirc x+ 7y = 20$

Possible Answers:

$-\frac{35}{4}$

$\frac{5}{28}$

$\frac{4}{35}$

None of the other responses is correct.

$-\frac{28}{5}$

Correct answer:

$-\frac{28}{5}$

Explanation:

Let be that missing coefficient. Then the equation can be rewritten as

Ax+ 7y = 20

Put the equation in slope-intercept form:

7y = -Ax + 20

$\frac{7y }{7}=\frac{ -Ax + 20}{7}$

$y =- \frac{ A }{7}x+ \frac{ 20}{7}$

The coefficient of is the slope, so solve for in the equation

$- \frac{ A }{7} =\frac{4}{5}$

$- \frac{ A }{7} \cdot (-7)=\frac{4}{5} \cdot (-7)$

$A=-\frac{28}{5}$

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Example Question #692 : Geometry

Fill in the circle with a number so that the graph of the resulting equation has slope 4:

$5 y = \bigcirc x + 4$

Possible Answers:

$\frac{4}{5}$

$\frac{5}{4}$

Correct answer:

Explanation:

Let be that missing coefficient. Then the equation can be rewritten as

5 y = Ax + 4

Put the equation in slope-intercept form:

$\frac{5 y}{5} =\frac{ Ax + 4}{5}$

$y = \frac{A}{5}x + \frac{4}{5}$

The coefficient of is the slope, so solve for in the equation

$\frac{A}{5} = 4$

$\frac{A}{5}\cdot 5 = 4 \cdot 5$

A = 20

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Example Question #94 : Coordinate Geometry

Examine these two equations.

5 x - 3 y = 9

$\square y = x + 7$

Write a number in the box so that the lines of the two equations will have the same slope.

Possible Answers:

$\frac{3}{5}$

$\frac{5}{9}$

$\frac{9}{5}$

$\frac{5}{3}$

Correct answer:

$\frac{3}{5}$

Explanation:

Write the first equation in slope-intercept form:

5 x - 3 y = 9

5 x - 3 y +3y - 9 = 9+3y - 9

3y = 5x-9

$\frac{3y}{3} = \frac{5x-9}{3}$

$y = \frac{5}{3}x - 3$

The coefficient of , which here is $\frac{5}{3}$ , is the slope of the line.

Now, let be the nuimber in the box, and rewrite the second equation as

A y = x + 7

Write in slope-intercept form:

$\frac{A y }{A}= \frac{x + 7}{A}$

$y = \frac{1}{A}x+\frac{7}{A}$

The slope is $\frac{1}{A}$ , which is set to $\frac{5}{3}$ :

$\frac{1}{A}= \frac{5}{3}$

$A= \frac{3}{5}$

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Example Question #693 : Geometry

Fill in the circle with a number so that the graph of the resulting equation is a horizontal line:

$y = x + \bigcirc$

Possible Answers:

The graph is a horizontal line no matter what number is written.

The graph cannot be a horizontal line no matter what number is written.

is the only number that works.

Correct answer:

The graph cannot be a horizontal line no matter what number is written.

Explanation:

The equation of a horizontal line takes the form y = b for some value of . Regardless of what is written, the equation cannot take this form.

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Example Question #13 : Calculating The Slope Of A Line

Fill in the square and the circle with two numbers so that the line of resulting equation has slope $-\frac{3 }{5}$ :

$\square x + 4y = \bigcirc$

Possible Answers:

None of the other responses is correct.

$\frac{12}{5}$ in the square and $\frac{4}{7}$ in the circle

$\frac{20}{3}$ in the square and $\frac{3}{7}$ in the circle

$-\frac{12}{5}$ in the square and $-\frac{3}{7}$ in the circle

$-\frac{20}{3}$ in the square and $-\frac{4}{7}$ in the circle

Correct answer:

$\frac{12}{5}$ in the square and $\frac{4}{7}$ in the circle

Explanation:

Let and be those missing numbers. Then the equation can be rewritten as

A x + 4y = C

Put the equation in slope-intercept form:

4y =-Ax+ C

$\frac{4y}{4} =\frac{-Ax+ C}{4}$

$y =-\frac{A}{4}x + \frac{ C}{4}$

The coefficient of is the slope, so solve for in the equation

$-\frac{A}{4} = -\frac{3}{5}$

$-\frac{A}{4} \cdot (-4) = -\frac{3}{5} \cdot (-4)$

$A = \frac{12}{5}$

The number in the circle is irrelevant, so the correct choice is that $\frac{12}{5}$ goes in the square and $\frac{4}{7}$ goes in the circle.

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Example Question #694 : Geometry

Fill in the circle with a number so that the graph of the resulting equation has slope 4:

$y = 6x + \bigcirc$

Possible Answers:

$\frac{3}{2}$

$-\frac{3}{2}$

It is impossible to do this.

Correct answer:

It is impossible to do this.

Explanation:

Once a number is filled in, the equation will be in slope-intercept form

y = mx+b ,

so the coefficient of will be the slope of the line of the equation. Regardless of the number that is written in the circle, this coefficient, and the slope, will be 6, so the slope cannot be 4.

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Example Question #15 : Calculating The Slope Of A Line

Consider segment $\overline{JK}$ which passes through the points $\left ( 4,5\right )$ and $\left ( 144,75\right )$ .

What is the slope of $\overline{JK}$ ?

Possible Answers:

$\small \frac{3}{4}$

$\small 2$

$\small \frac{2}{3}$

$\small \frac{1}{2}$

$\small -\frac{1}{2}$

Correct answer:

$\small \frac{1}{2}$

Explanation:

Slope is found via:

$\small m=\frac{y'-y}{x'-x}$

Plug in and calculate:

$\small \small m=\frac{75-5}{144-4}=\frac{70}{140}=\frac{1}{2}$

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Example Question #695 : Geometry

What is the -intercept of the line x + 2Ay = 4A ?

Possible Answers:

(4,0)

(4A,0)

$\left ( \frac{A}{4},0 \right )$

$\left ( \frac{1}{4},0 \right )$

$\left ( \frac{4}{A},0 \right )$

Correct answer:

(4A,0)

Explanation:

To solve for the x-intercept, substitute 0 for and solve for :

x + 2Ay = 4A

$x+ 2A \cdot 0= 4A$

x= 4A

The -intercept is (4A,0) .

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GMAT Math : Geometry

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #691 : Geometry

Example Question #91 : Coordinate Geometry

Example Question #92 : Coordinate Geometry

Example Question #692 : Geometry

Example Question #94 : Coordinate Geometry

Example Question #693 : Geometry

Example Question #13 : Calculating The Slope Of A Line

Example Question #694 : Geometry

Example Question #15 : Calculating The Slope Of A Line

Example Question #695 : Geometry

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