GMAT Math : GMAT Quantitative Reasoning

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Example Questions

Example Question #17 : Algebra

Given 5x-7y=-2 and 8y-x=7 , find the values of and .

Possible Answers:

x=1, y=1

x=-1, y=1

x=2, y=-1

x=4, y=-1

Correct answer:

x=1, y=1

Explanation:

We can solve this problem by setting up a system of equations and using elimination:

5x-7y=-2

8y-x=7

We can eliminate the and solve for by multiplying the bottom equation by and adding the equations:

5x-7y=-2

-5x+40y=35

___________________

33y=33

y=1

We can now find by substituting our into any equation:

8(1)-x=7

8-7=x

x=1

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Example Question #1101 : Gmat Quantitative Reasoning

The product of two positive numbers, and , yields . If their sum is , what is the value of ?

Possible Answers:

$\textup{More information is required to solve this problem.}$

Correct answer:

$\textup{More information is required to solve this problem.}$

Explanation:

We have enough information to write out two equations:

$n\cdot p=24$

n+p=11

Using the first equation, we can narrow our potential values to: $\textup{ 1 and 24, 2 and 12, 3 and 8, and 4 and 6}$ .

Using the second equation, we can narrow down our values even further to $\textup{3 and 8}$ . We are, however, being asked specifically for the value of . Since we cannot state if the or the represents and which represents , we cannot answer this question. Additional data, such as is less than , would be required.

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Example Question #14 : Algebra

Solve for .

3x-2y=16

-2x+3y=-4

Possible Answers:

10.5

Correct answer:

Explanation:

We can solve this problem in the same way we would solve a system of equations using elimination. Since we are solving for we can manipulate the system to cancel out the values: 3(3x-2y=16) 9x-6y=48

2(-2x+3y=-4) -4x+6y=-8

We then add the equations. Notice how the values cancel out 5x=40

leaving us with x=8

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Example Question #21 : Solving Linear Equations With Two Unknowns

Solve the following system of equations:

x+y=7

x-y=3

Possible Answers:

x=5,y=2

x=4,y=3

x=3,y=4

x=2,y=5

Correct answer:

x=5,y=2

Explanation:

To solve, I used the elimination method by adding the tqo equations together. That eliminates y and leaves you with:

$2x=10\Rightarrow x=5$

Therefore,

$(5)+y=7\Rightarrow y=2$

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Example Question #22 : Algebra

Which of the following equations is parallel to the line given by the equation:

$y = \frac{-4}{3}x + 15$

Possible Answers:

-6y = 8x + 18

$y = \frac{3}{4}x +15$

-4y = 3x + 15

3y = -8x + 15

-3y = 45 - 4x

Correct answer:

-6y = 8x + 18

Explanation:

For lines to be parallel, their equations must have equal slopes. Therefore, we are looking for another line with a slope of -4/3. If we convert the equation:

-6y = 8x + 18

into slope - intercept form, we get:

$\frac{-6y}{-6} = \frac{8x}{-6} + \frac{18}{-6}$

$y = \frac{-8}{6}x - 3 = y = \frac{-4}{3}x - 3$

It has the same slope, and therefore is parallel to the original line.

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Example Question #1102 : Gmat Quantitative Reasoning

The equations -6y = 3x + 18 and 4y = -8x + 12 intersect at the point (4, y) . What is y?

Possible Answers:

$\frac{-1}{5}$

$\frac{1}{5}$

Correct answer:

Explanation:

The easiest way to solve the problem is to solve for y in one of the equations and then plug it into the other equation:

$\frac{4y}{4} = \frac{-8x}{4} + \frac{12}{4} = y = -2x + 3$

-6(-2x + 3) = 3x + 18 12x - 3x - 18 + 18 = 3x -3x + 18 + 18

9x = 36

x = 4

We can then plug that x-value into one of the original equations:

4y = -8(4) + 12

$\frac{4y}{4} = \frac{-32 + 12}{4} = y= \frac{-20}{4} = -5$

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Example Question #1 : Exponents

$\frac{6^{3}}{36} + \frac{3^{68}}{3^{67}}=$

Possible Answers:

$\dpi{100} \small 18$

$\dpi{100} \small 36$

cannot be determined

$\dpi{100} \small 9$

$\dpi{100} \small 6$

Correct answer:

$\dpi{100} \small 9$

Explanation:

$\frac{6^{3}}{36} = \frac{6^{3}}{6^{2}} = 6$

$\frac{3^{68}}{3^{67}} = 3^{68-67} = 3$

Putting these together,

$\frac{6^{3}}{36} + \frac{3^{68}}{3^{67}}= 6 + 3 = 9$

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Example Question #1 : Exponents

$\dpi{100} \small 3x^{4}\times x^{2}+x^{2}-x =$

Possible Answers:

$x(3x^{5}-x+1)$

$x(3x^{5}+x-1)$

$3x^{7}$

$3x^{9}$

$3x^{5}+x-1$

Correct answer:

$x(3x^{5}+x-1)$

Explanation:

$\dpi{100} \small 3x^{4}\times x^{2} =3x^{6}$

Then, $\dpi{100} \small 3x^{4}\times x^{2}+x^{2}-x = 3x^{6}+x^{2}-x = x(3x^{5}+x-1)$

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Example Question #1 : Understanding Exponents

$4^{\frac{3}{2}} + 27^{\frac{2}{3}} =$

Possible Answers:

$\dpi{100} \small 8$

$\dpi{100} \small 27$

$\dpi{100} \small 16$

$\dpi{100} \small 9$

$\dpi{100} \small 17$

Correct answer:

$\dpi{100} \small 17$

Explanation:

$4^{\frac{3}{2}}=(4^{\frac{1}{2}})^{3} = 2^{3} = 8$

$27^{\frac{2}{3}}=(27^{\frac{1}{3}})^{2} = 3^{2} = 9$

Then putting them together, $4^{\frac{3}{2}} + 27^{\frac{2}{3}} = 8 + 9 = 17$

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Example Question #2 : Understanding Exponents

Which of the following expressions is equivalent to this expression?

$\small \frac{x^{-\frac{1}{2}}}{x^{\frac{1}{3}}}$

You may assume that $\small x > 0$ .

Possible Answers:

$\small \small \small \frac{\sqrt[5]{x^{6}}}{x}$

$\small x\sqrt{x}$

$\small \frac{\sqrt[6]{x}}{x}$

$\small \sqrt[3]{x^{2}}$

$\small \small \frac{\sqrt[6]{x^{5}}}{x}$

Correct answer:

$\small \frac{\sqrt[6]{x}}{x}$

Explanation:

$\small \small \small \small \small \small \small \small \small \frac{x^{-\frac{1}{2}}}{x^{\frac{1}{3}}} = x^{-\frac{1}{2} -{\frac{1}{3}} } = x^{-\frac{2}{6} -{\frac{3}{6}} }= x^{-\frac{5}{6} }= \frac{1}{ x^{\frac{5}{6}}}$

$\small \small \small = \frac{1}{\sqrt[6]{x^{5}}}= \frac{\sqrt[6]{x}}{\sqrt[6]{x^{5}}\cdot \sqrt[6]{x}}= \frac{\sqrt[6]{x}}{x}$

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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 #17 : Algebra

Example Question #1101 : Gmat Quantitative Reasoning

Example Question #14 : Algebra

Example Question #21 : Solving Linear Equations With Two Unknowns

Example Question #22 : Algebra

Example Question #1102 : Gmat Quantitative Reasoning

Example Question #1 : Exponents

Example Question #1 : Exponents

Example Question #1 : Understanding Exponents

Example Question #2 : Understanding Exponents

All GMAT Math Resources

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