GMAT Math : Solving equations

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #21 : Equations

Give the solution set of the equation: 

Possible Answers:

Correct answer:

Explanation:

Case 1: 

Then , and the equation becomes

 

Case 2: 

Then , and the equation becomes

However, this conflicts with the fact that , so this is a false solution.

 

The only solution is therefore .

Example Question #22 : Equations

Give the solution set of the equation:

Possible Answers:

Correct answer:

Explanation:

Case 1:  is nonnegative - that is, .

The equation becomes 

Either , in which case ,

or , in which case , which is impossible, as we are assuming that  is nonnegative.

case 2:  is negative - that is, 

The equation becomes 

Either , in which case , which is impossible since we are assuming that  is negative, 

or , in which case .

 and  can both be confirmed as solutions.

Example Question #23 : Equations

What is the equation of the line that goes through  and is parallel to ?

Possible Answers:

Correct answer:

Explanation:

First, we have to find the slope from  using the general form  Therefore

Parallel lines have the same slope, so the new line has a slope of  and point .

Use the point-slope equation: 

Example Question #24 : Equations

What is the -intercept of ?

Possible Answers:

Correct answer:

Explanation:

To solve for the -intercept, you set the  to zero and solve for :

 

-intercept: 

Example Question #25 : Equations

What is the y-intercept of ?

Possible Answers:

Correct answer:

Explanation:

To solve for the y-intercept, you set  to zero and solve for :

 

Therefore, the y-intercept is: 

Example Question #26 : Equations

What is the -intercept of ?

Possible Answers:

Correct answer:

Explanation:

To solve for the -inter, you set  to zero and solve for :

 

x-intercept:

Example Question #1421 : Problem Solving Questions

What is the y-intercept of ?

Possible Answers:

Correct answer:

Explanation:

To solve for the y-intercept of , you set  to zero and solve for :

 

y-intercept: 

Example Question #1421 : Problem Solving Questions

To convert Fahrenheit temperature  to the equivalent in Celsius , use the formula 

To the nearest tenth of a degree, convert  to degrees Celsius.

Possible Answers:

Correct answer:

Explanation:

Example Question #28 : Equations

Solve for :

Possible Answers:

The equation has no solution.

Correct answer:

Explanation:

Rewrite as a compound equation, then solve each equation individually:

 

or

Example Question #30 : Solving Equations

Solve for :

Possible Answers:

The equation has no solution.

Correct answer:

Explanation:

Eliminate the denominators by multiplying by , then solve the resulting equation:

Solve using the  method:

 

or

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