GRE Math : How to evaluate algebraic expressions

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #41 : How To Evaluate Algebraic Expressions

Quantity A: 

Quantity B: 

Possible Answers:

The relationship cannot be determined.

Quantity B is greater.

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:

 

Quantity A:

Since this is , it can have the values of  or . Both are bigger than 

Quantity A is greater.

Example Question #42 : How To Evaluate Algebraic Expressions

Quantity A: 

Quantity B: 

Possible Answers:

The relationship cannot be determined.

The two quantities are equal.

Quantity A is greater.

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:

Quantity A:

The two possible values are . Only one of them is greater than five.

The relationship cannot be determined.

Example Question #43 : How To Evaluate Algebraic Expressions

Quantity A: 

Quantity B: 

Possible Answers:

The two quantities are equal.

The relationship cannot be determined.

Quantity A is greater.

Quantity B is greater.

Correct answer:

Quantity B is greater.

Explanation:

Since there is an  term in the equation

 

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

For an equation of the form

The solutions for  can be found using the quadratic formula:

Both roots are negative.

Quantity B is greater.

Example Question #44 : How To Evaluate Algebraic Expressions

At a store, pasta is sold in three sizes. A large box costs the same as four medium boxes or eight small boxes. If James buys an equal amount of large and medium boxes of pasta for the price needed to buy one hundred small boxes, how many medium boxes of pasta does he buy?

Possible Answers:

Correct answer:

Explanation:

To approach this problem, assign variables. Since one large box equals four medium boxes or eight small boxes in price

From this we can say that

or that

We're told that James buys an equal number of large and medium boxes, and that the total price is equal to that of 100 small boxes:

Rewrite this equation in terms of just the price of small boxes:

James buys ten medium and ten large boxes of large pasta.

 

Example Question #81 : Expressions

When the integer  is multiplied by , the result is  more than  times the integer . What is  ?

Possible Answers:

Correct answer:

Explanation:

The key is to write the problem into mathematical terms.

We're told

"When the integer  is multiplied by , the result is  more than  times the integer ."

Breaking this down piece by piece:

When the integer  is multiplied by 

When the integer  is multiplied by , the result is : 

When the integer  is multiplied by , the result is  more than: 

When the integer  is multiplied by , the result is  more than  times the integer :

Now, solve this for 

Example Question #46 : How To Evaluate Algebraic Expressions

Quantity A: 

Quantity B: 

Possible Answers:

The relationship cannot be determined.

The two quantities are equal.

Quantity B is greater.

Quantity A 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:

Quantity A can be either three or four. Since one of these is equal to Quantity B while the other is greater, the relationship cannot be determined. 

Example Question #47 : How To Evaluate Algebraic Expressions

When the integer  is multiplied by , the result is thrice the difference of  and  times the integer . What is the value of  ?

Possible Answers:

Correct answer:

Explanation:

To approach this problem, write out the problem statement in mathematical terms.

We're told

"When the integer  is multiplied by , the result is thrice the difference of  and  times the integer ."

Write this out step by step.

When the integer  is multiplied by :

When the integer  is multiplied by , the result is:

When the integer  is multiplied by , the result is thrice:

When the integer  is multiplied by , the result is thrice the difference:

When the integer  is multiplied by , the result is thrice the difference of :

When the integer  is multiplied by , the result is thrice the difference of  and  times the integer :

Now, solve for 

Example Question #48 : How To Evaluate Algebraic Expressions

Quantity A: 

Quantity B: 

Possible Answers:

The relationship cannot be determined.

The two quantities are equal.

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:

Both possible values for Quantity A are greater than  

Quantity A is greater. 

 

Example Question #49 : How To Evaluate Algebraic Expressions

Take the expression  to be equivalent to . What is the expression  equivalent to?

Possible Answers:

Correct answer:

Explanation:

When considering  , begin at the right of the equation. Since

  is equivalent to  must be equivalent to

Now we need only consider 

Example Question #41 : How To Evaluate Algebraic Expressions

 

Quantity A: 

Quantity B: 

Possible Answers:

Quantity A is greater.

The two quantities are equal.

Quantity B is greater.

The relationship cannot be determined.

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 there are two roots for x, Quantity A has two possible values:

Both of these are greater than .

Quantity A is greater.

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