GMAT Math : Problem-Solving Questions

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Example Questions

Example Question #2 : Calculating Whether Lines Are Perpendicular

A given line has a slope of m=6 . What is the slope of any line perpendicular to ?

Possible Answers:

Not enough information provided

$-\frac{1}{6}$

Correct answer:

$-\frac{1}{6}$

Explanation:

In order for a line to be perpendicular to another line defined by the equation y=mx+b , the slope of line must be a negative reciprocal of the slope of line . Since line 's slope is in the slope-intercept equation above, line 's slope would therefore be $-\frac{1}{m}$ .

Given that we have a line with a slope m=6 , we can therefore conclude that any perpendicular line would have a slope $-\frac{1}{m}=-\frac{1}{6}$ .

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Example Question #3 : Calculating Whether Lines Are Perpendicular

Which of the following lines are perpendicular to $y=\frac{5}{6}x+10$ ?

Possible Answers:

$y=-\frac{6}{5}x-7$

Two answers are perpendicular to the given line.

$y=-\frac{5}{6}x-2$

$y=\frac{5}{6}x-7$

$y=-\frac{6}{5}x+10$

Correct answer:

Two answers are perpendicular to the given line.

Explanation:

Since in this instance the slope $m=\frac{5}{6}$ , $-\frac{1}{m}=-\frac{1}{\frac{5}{6}}=-\frac{6}{5}$ . Two of the above answers have this as their slope, so therefore that is the answer to our question.

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Example Question #4 : Calculating Whether Lines Are Perpendicular

Do the functions f(x) and g(x) intersect at a ninety-degree angle, and how can you tell?

$\small f(x)=3x+7$

$\small g(x)=-\frac{1}{3}x+7$

Possible Answers:

It is impossible to determine from the information provided.

Yes, because f(x) and g(x) have the same y-intercept.

No, because f(x) and g(x) never intersect.

Yes, because the slope of g(x) is the reciprocal of the slope of f(x) and it has the opposite sign.

No, because f(x) and g(x) have different slopes.

Correct answer:

Yes, because the slope of g(x) is the reciprocal of the slope of f(x) and it has the opposite sign.

Explanation:

If two lines intersect at a ninety-degree angle, they are said to be perpendicular. Two lines are perpendicular if their slopes are opposite reciprocals. In this case:

$f(x)\:slope=\frac{3}{1}$

$g(x)\:slope=-\frac{1}{3}$

The two lines' slopes are reciprocals with opposing signs, so the answer is yes. Of our two yes answers, only one has the right explanation. Eliminate the option dealing with -intercepts.

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Example Question #5 : Calculating Whether Lines Are Perpendicular

Find the slope of a line that is perpendicular to the line running through the points (7,4) and (5,8) .

Possible Answers:

$\frac{1}{2}$

$-\frac{1}{2}$

Not enough information provided.

Correct answer:

$\frac{1}{2}$

Explanation:

To find the slope of the line running through (7,4) and (5,8) , we use the following equation:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{8-4}{5-7}=\frac{4}{-2}=-2$

The slope of any line perpendicular to the given line would have a slope that is the negative reciprocal of , or $-\frac{1}{m}$ . Therefore, $-\frac{1}{-2}=\frac{1}{2}$

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Example Question #11 : Calculating Whether Lines Are Perpendicular

Which of the following lines is perpendicular to $y=\frac{3}{4}x+16$ ?

Possible Answers:

Not enough information provided.

$y=\frac{3}{4}x+7$

$y=\frac{4}{3}x+8$

$y=-\frac{4}{3}x+12$

$y=\frac{3}{4}x-6$

Correct answer:

$y=-\frac{4}{3}x+12$

Explanation:

Given a line defined by the equation y=mx+b with a slope of , any line perpendicular to would have a slope that is the negative reciprocal of , $-\frac{1}{m}$ . Given our equation $y=\frac{3}{4}x+16$ , we know that $m=\frac{3}{4}$ and that $-\frac{1}{m}=-\frac{1}{\frac{3}{4}}=-\frac{4}{3}$ .

The only answer choice with this slope is $y=-\frac{4}{3}x+12$ .

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Example Question #631 : Problem Solving Questions

Which of the following lines is perpendicular to y=5x-12

Possible Answers:

$y=-\frac{1}{5}x-4$

$y=\frac{1}{5}x-6$

Two of the answers are correct.

$y=\frac{1}{5}x+19$

$y=-\frac{1}{5}x+7$

Correct answer:

Two of the answers are correct.

Explanation:

Given a line defined by the equation y=mx+b with a slope of , any line perpendicular to would have a slope that is the negative reciprocal of , $-\frac{1}{m}$ . Given our equation y=5x-12 , we know that m=5 and that $-\frac{1}{m}=-\frac{1}{5}$ .

There are two answer choices with this slope, $y=-\frac{1}{5}x-4$ and $y=-\frac{1}{5}x+7$ .

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Example Question #13 : Lines

A given line is defined by the equation y=2x+5 . Which of the following lines would be perpendicular to line ?

Possible Answers:

$y=-\frac{1}{2}x+7$

y=2x+14

y=-2x+7

Not enough information provided

$y=\frac{1}{2}x+7$

Correct answer:

$y=-\frac{1}{2}x+7$

Explanation:

For any line with an equation y=mx+b and slope , a line that is perpendicular to must have a slope of $-\frac{1}{m}$ , or the negative reciprocal of . Given y=2x+5 , we know that m=2 and therefore know that $-\frac{1}{m}=-\frac{1}{2}$ .

Only one equation above has a slope of $-\frac{1}{2}$ : $y=-\frac{1}{2}x+7$ .

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Example Question #14 : Lines

What is the slope of a line that is perpendicular to $y=-\frac{1}{7}x+9$

Possible Answers:

$\frac{1}{9}$

$-\frac{1}{9}$

Correct answer:

Explanation:

For any line with an equation y=mx+b and slope , a line that is perpendicular to must have a slope of $-\frac{1}{m}$ , or the negative reciprocal of . Given the equation $y=-\frac{1}{7}x+9$ , we know that $m=-\frac{1}{7}$ and therefore know that $-\frac{1}{m}=-\frac{1}{-\frac{1}{7}}=7$ .

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Example Question #12 : Calculating Whether Lines Are Perpendicular

Which of the following lines is perpendicular to y=4x+8 ?

Possible Answers:

Two lines are perpendicular

$y=-\frac{1}{4}x+5$

$y=4x-\frac{1}{8}$

$y=-\frac{1}{4}x-4$

None of the lines is perpendicular

Correct answer:

Two lines are perpendicular

Explanation:

For any line with an equation y=mx+b and slope , a line that is perpendicular to must have a slope of $-\frac{1}{m}$ , or the negative reciprocal of . Given the equation y=4x+8 , we know that m=4 and therefore know that $-\frac{1}{m}=-\frac{1}{4}$ .

Given a slope of $-\frac{1}{4}$ , we know that there are two solutions provided: $y=-\frac{1}{4}x+5$ and $y=-\frac{1}{4}x-4$ .

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Example Question #401 : Geometry

What is the slope of a line perpendicular to that of 6y-3x=2?

Possible Answers:

$\frac{-1}{2}$

$\frac{1]}{2}$

Correct answer:

Explanation:

First, we need to rearrange the equation into slope-intercept form. y=mx+b .

$6y-3x=2->y=\frac{3x+2}{6}.$ Therefore, the slope of this line equals $\frac{1}{2}.$ Perpendicular lines have slope that are the opposite reciprocal, or -2.

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GMAT Math : Problem-Solving Questions

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #2 : Calculating Whether Lines Are Perpendicular

Example Question #3 : Calculating Whether Lines Are Perpendicular

Example Question #4 : Calculating Whether Lines Are Perpendicular

Example Question #5 : Calculating Whether Lines Are Perpendicular

Example Question #11 : Calculating Whether Lines Are Perpendicular

Example Question #631 : Problem Solving Questions

Example Question #13 : Lines

Example Question #14 : Lines

Example Question #12 : Calculating Whether Lines Are Perpendicular

Example Question #401 : Geometry

All GMAT Math Resources

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