GRE Math : How to evaluate algebraic expressions

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #51 : How To Evaluate Algebraic Expressions

Quantity A: 

Quantity B: 

Possible Answers:

The two quantities are equal.

The relationship cannot be determined.

Quantity B is larger.

Quantity A is larger.

Correct answer:

Quantity A is larger.

Explanation:

Since there is an  term in the equation

 

We must acknowledge the possibility of multiple values that satisfy the equation.

Rewrite it so that it is set equal to zero:

 

For an equation of the form

The solutions for  can be found using the quadratic formula:

The two possible values for Quantity A are

Since , Quantity A must be larger.

Example Question #51 : How To Evaluate Algebraic Expressions

The expression  is equivalent to . Evaluate 

Possible Answers:

Correct answer:

Explanation:

Since  is equivalent to , we can rewrite  as

Example Question #53 : How To Evaluate Algebraic Expressions

The expression  is equivalent to . Evaluate the expression .

Possible Answers:

Correct answer:

Explanation:

To approach this problem, do it in parts, starting at the right of the equation.

If expression  is equivalent to , then

 then becomes 

Example Question #54 : How To Evaluate Algebraic Expressions

Quantity A: 

Quantity B: 

Possible Answers:

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined.

Quantity A is greater.

Correct answer:

The two quantities are equal.

Explanation:

Since there is an  term in the equation

 

We must acknowledge the possibility of multiple values that satisfy the equation.

Rewrite it so that it is set equal to zero:

 

For an equation of the form

The solutions for  can be found using the quadratic formula:

Since , it must be that 

The two quantities are equal.

Example Question #55 : How To Evaluate Algebraic Expressions

Quantity A: 

Quantity B: 

Possible Answers:

Quantity A is greater.

The relationship cannot be determined.

Quantity B is greater.

The two quantities are equal.

Correct answer:

Quantity A is greater.

Explanation:

Since there is an  term in the equation

 

We must acknowledge the possibility of multiple values that satisfy the equation.

Rewrite it so that it is set equal to zero:

 

For an equation of the form

The solutions for  can be found using the quadratic formula:

Since , it must be that 

Quantity A is greater.

Example Question #371 : Gre Quantitative Reasoning

If  and , all of the of following are equal to  except?

Possible Answers:

Correct answer:

Explanation:

A way to approach this problem is to realize that the coefficient for  should be twice whatever coefficient is multiplied by  in the parenthesis, and to look for a case where that does not hold true.

In the case of 

The coffecient for  is  times the coefficient for , rather than twice it, and so there is no way this could satisfy the condition of .

This method of evaluation saves the trouble of multiplying each function out to check for equivalency.

Example Question #51 : How To Evaluate Algebraic Expressions

Quantity A: 

Quantity B: 

Possible Answers:

The relationship cannot be determined.

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

Correct answer:

Quantity A is greater.

Explanation:

Since there is an  term in the equation

We must acknowledge the possibility of multiple values that satisfy the equation.

Rewrite it so that it is set equal to zero:

For an equation of the form

The solutions for  can be found using the quadratic formula:

Now there are two potential values for , both of which are negative. Consider our quantities. For both of these values, Quantity A is greater.

 

Example Question #53 : How To Evaluate Algebraic Expressions

Quantity A: 

Quantity B: 

Possible Answers:

The two quantities are equal.

The relationship cannot be determined.

Quantity B is greater.

Quantity A is greater.

Correct answer:

Quantity A is greater.

Explanation:

Since there is an  term in the equation

We must acknowledge the possibility of multiple values that satisfy the equation.

Rewrite it so that it is set equal to zero:

For an equation of the form

The solutions for  can be found using the quadratic formula:

So there are two possible values for , one negative and one positive. Let's consider our quantities for these two possibilities.

Even though we have a positive value for one of the values of , since it is less than one, the cube of it is smaller than it is.

Quantity A is greater.

Example Question #59 : How To Evaluate Algebraic Expressions

Quantity A: 

Quantity B: 

Possible Answers:

The two quantities are equal.

Quantity A is greater.

The relationship cannot be determined.

Quantity B is greater.

Correct answer:

The relationship cannot be determined.

Explanation:

Since there is an  term in the equation

We must acknowledge the possibility of multiple values that satisfy the equation.

Rewrite it so that it is set equal to zero:

For an equation of the form

The solutions for  can be found using the quadratic formula:

So there are two possible values of , both of which are positive. Compare the two quantities for each potential value:

Depending on the value of , Quantity A or B could be greater. The relationship cannot be determined.

Example Question #54 : How To Evaluate Algebraic Expressions

Quantity A: 

Quantity B: 

Possible Answers:

Quantity B is greater.

The relationship cannot be determined.

The two quantities are equal.

Quantity A is greater.

Correct answer:

Quantity A is greater.

Explanation:

Since there is an  term in the equation

We must acknowledge the possibility of multiple values that satisfy the equation.

Rewrite it so that it is set equal to zero:

For an equation of the form

The solutions for  can be found using the quadratic formula:

Both values of  are positive, so we can't just say  is greater! Compare the two quantities:

Since both values of  are greater than zero and less than one, their squares are less than they are.

Quantity A is greater.

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