GMAT Math : Solving equations

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Example Questions

Example Question #381 : Algebra

D = E - 12

$E = \sqrt{F}$

F = 2 G

Express in terms of .

Possible Answers:

$G = \sqrt{2D}- 12$

$G = 4D^{2} - 96D + 576$

$G = \sqrt{2D-24}$

$G = \frac{1}{2} D^{2} -12D +72$

$G = \frac{1}{2} D^{2} +12D +72$

Correct answer:

$G = \frac{1}{2} D^{2} +12D +72$

Explanation:

F = 2 G

$F\div 2 = 2 G \div 2$

$\frac{1}{2} F = G$

$E = \sqrt{F}$

$E^{2} = (\sqrt{F})^{2}$

$E^{2} =F$

D = E - 12

D + 12 = E - 12 + 12

D + 12 = E

By two substitutions:

$G = \frac{1}{2} F = \frac{1}{2} E^{2} = \frac{1}{2} (D+12)^{2}$

$G = \frac{1}{2} (D^{2} +2 \cdot 12 \cdot D +12^{2})$

$G = \frac{1}{2} (D^{2} +24 D +144)$

$G = \frac{1}{2} D^{2} +12D +72$

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Example Question #71 : Solving Equations

Which of the following is the solution set of the equation:

$x-3 = \sqrt{2x+9}$

Possible Answers:

$\left \{ 0,8\right \}$

$\left \{ 0\right \}$

$\left \{ -8, 0\right \}$

$\left \{ -8\right \}$

$\left \{ 8\right \}$

Correct answer:

$\left \{ 8\right \}$

Explanation:

Square both sides of the equation, then solve the resulting quadratic equation by factoring:

$x-3 = \sqrt{2x+9}$

$\left (x-3 \right ) ^{2}=\left ( \sqrt{2x+9 \right )}^{2}$

$x^{2}-6x+9=2x+9$

$x^{2}-8x=0$

x(x-8)=0

Either x=0

x-8=0

x=8

Checking both solutions, however:

$0-3 = \sqrt{2\cdot 0+9}$

-3 = 3

This eliminates 0 as a solution.

$8-3 = \sqrt{2\cdot 8+9}$

5=5

8 turns out to be the only solution.

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GMAT Math : Solving equations

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #381 : Algebra

Example Question #71 : Solving Equations

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