GMAT Math : Solving equations

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Example Questions

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Example Question #41 :Equations

Solve for:

13+X-Y=2Y

Possible Answers:

X=-16Y

X=-13+3Y

X=10

X=13+-3Y

X=16Y

Correct answer:

X=-13+3Y

Explanation:

13+X-Y=2Y

We need to isolate. Move all other terms to the right hand side of the equation:

13+X-Y-13+Y=2Y-13+Y

Combine like terms:

X=-13+3Y

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Example Question #351 :Algebra

Solve for the value of:

|x-4|=-3x+5

Possible Answers:

$(\frac{4}{9},\frac{1}{2})$

$(\frac{9}{4},\frac{1}{2})$

$(-\frac{1}{2}, \frac{9}{4})$

$(\frac{5}{4},\frac{3}{2})$

$(-\frac{9}{4},\frac{1}{2})$

Correct answer:

$(\frac{9}{4},\frac{1}{2})$

Explanation:

|x-4|=-3x+5

To solve this absolute value equation, we need to set the right side of the equation equal to a positive and negative version in order to calculate the two options for absolute value.

x-4=-3x+5 OR x-4=-(-3x+5)=3x-5

x+3x=5+4 OR x-3x=-5+4

4x=9 OR -2x=-1

$x=\frac{9}{4}$ OR $x=\frac{1}{2}$

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Example Question #1439 :Problem Solving Questions

4-n=5

5m-8=12+3m

You are given the equations above. What is m-n ?

Possible Answers:

Correct answer:

Explanation:

We first solve each of the equations to findand:

4-n=5

-n=5-4

n=-1

5m-8=12+3m

5m-3m=12+8

2m=20

m=10

m-n=10-(-1)=10+1=11

Therefore, m-n=11 .

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Example Question #1440 :Problem Solving Questions

You are given the following equation:

$x=\frac{x-6}{3+x}$

What is the value of $x^{2}+2x+3$ ?

Possible Answers:

Correct answer:

Explanation:

First, we need to solve the provided equation for.

$x=\frac{x-6}{3+x}$

x(3+x)=x-6

$3x+x^{2}=x-6$

$3x+x^{2}-x=-6$

$x^{2}+2x+6=0$

We want to find the value of $x^{2}+2x+3$ . We can put the equation in this form by subtractingfrom each side:

$x^{2}+2x+6-3=-3$

$x^{2}+2x+3=-3$

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Example Question #41 :Solving Equations

Solve $\left | 2x+12\right |=20$ .

Possible Answers:

x=4 or x=-16

x=8

x=-16

x=4

x=8 or x=-16

Correct answer:

x=4 or x=-16

Explanation:

Since we are solving an absolute value equation, $\left | 2x+12\right |=20$ , we must solve for both potential values of the equation:

1.) 2x+12=20

2.) 2x+12=-20

Solving Equation 1:

2x+12=20

2x=8

x=4

Solving Equation 2:

2x+12=-20

2x=-32

x=-16

Therefore, for $\left | 2x+12\right |=20$ , x=4 or x=-16 .

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Example Question #42 :Solving Equations

Solve for: 3y-4x=7x+33

Possible Answers:

$y=\frac{3}{11}x+11$

$y=-\frac{3}{11}x+11$

$y=-\frac{11}{3}x+11$

$y=\frac{11}{3}x+11$

Not enough information provided

Correct answer:

$y=\frac{11}{3}x+11$

Explanation:

In order to solve 3y-4x=7x+33 for, we need to isolateon one side of the equation:

3y-4x=7x+33

3y=11x+33

$y=\frac{11}{3}x+11$

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Example Question #43 :Solving Equations

Which of the following is a solution to the equation 7x+3y=22 ?

Possible Answers:

x=1, y=5

x=4, y=2

Two of the other answers are correct.

x=5, y=1

x=2, y=3

Correct answer:

x=1, y=5

Explanation:

In order to find values ofandfor which 7x+3y=22 , we need to plug the values into the equation:

1.) x=1, y=5 : 7(1)+3(5)=7+15=22 Correct

2.) x=5, y=1 : 7(5)+3(1)=35+3=38 Incorrect

3.) x=2, y=3 : 7(2)+3(3)=14+9=23 Incorrect

4.) x=4, y=2 : 7(4)+3(2)=28+6=34 Incorrect

Therefore, the only correct answer is x=1, y=5 .

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Example Question #44 :Solving Equations

Solve for: $\frac{1}{3}x+\frac{2}{3}y=\frac{7}{9}$

Possible Answers:

$y=\frac{7}{3}-2x$

$x=\frac{2}{3}-7y$

Not enough information provided

$x=\frac{7}{3}-2y$

$x=\frac{3}{7}-2y$

Correct answer:

$x=\frac{7}{3}-2y$

Explanation:

In order to solve the equation for, we need to isolateon one side of the equation:

$\frac{1}{3}x+\frac{2}{3}y=\frac{7}{9}$

$\frac{1}{3}x=\frac{7}{9}-\frac{2}{3}y$

$x=\frac{21}{9}-2y$

Reducing the fraction,

$x=\frac{7}{3}-2y$

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Example Question #45 :Solving Equations

Solve forin the equation

3d + ad + y = 10

Possible Answers:

$d= \frac{10 - y-a }{3 }$

$d= \frac{10 - y+a }{3 }$

$d= \frac{y-10 }{3+a}$

$d= \frac{10 + y }{3+a}$

$d= \frac{10 - y }{3+a}$

Correct answer:

$d= \frac{10 - y }{3+a}$

Explanation:

3d + ad + y = 10

3d + ad + y - y= 10 - y

3d + ad = 10 - y

$\left (3 + a \right )d = 10 - y$

$\frac{\left (3 + a \right )d }{3+a}= \frac{10 - y }{3+a}$

$d= \frac{10 - y }{3+a}$

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Example Question #46 :Solving Equations

Solve forin the equation:

$v = 1+ \sqrt[3]{w-7}$

Possible Answers:

$w = v^{3} -3v^{2}+3v-8$

$w = v^{3} +6$

$w = v^{3} +3v^{2}+3v-6$

$w = v^{3} -3v^{2}+3v+6$

$w = v^{3} +3v^{2}+3v+8$

Correct answer:

$w = v^{3} -3v^{2}+3v+6$

Explanation:

$v = 1+ \sqrt[3]{w-7}$

$v- 1 = 1+ \sqrt[3]{w-7} - 1$

$\sqrt[3]{w-7} = v- 1$

$\left (\sqrt[3]{w-7}\right )^{3} = \left (v- 1 \right )^{3}$

$w-7= v^{3} -3v^{2}+3v-1$

$w-7+ 7= v^{3} -3v^{2}+3v-1 + 7$

$w = v^{3} -3v^{2}+3v+6$

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GMAT Math : Solving equations

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #41 :Equations

Example Question #351 :Algebra

Example Question #1439 :Problem Solving Questions

Example Question #1440 :Problem Solving Questions

Example Question #41 :Solving Equations

Example Question #42 :Solving Equations

Example Question #43 :Solving Equations

Example Question #44 :Solving Equations

Example Question #45 :Solving Equations

Example Question #46 :Solving Equations

All GMAT Math Resources

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