All GRE Math Resources
Example Questions
Example Question #41 : How To Evaluate Algebraic Expressions
Quantity A:
Quantity B:
The relationship cannot be determined.
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
Quantity A is greater.
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:
Quantity A is greater.
The two quantities are equal.
The relationship cannot be determined.
Quantity B is greater.
The relationship cannot be determined.
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:
Quantity A is greater.
Quantity B is greater.
The relationship cannot be determined.
The two quantities are equal.
Quantity B is greater.
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?
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 #364 : Algebra
When the integer is multiplied by , the result is more than times the integer . What is ?
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 #45 : How To Evaluate Algebraic Expressions
Quantity A:
Quantity B:
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined.
The relationship cannot be determined.
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 #46 : 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 ?
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 #47 : How To Evaluate Algebraic Expressions
Quantity A:
Quantity B:
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined.
Quantity A is greater.
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 #48 : How To Evaluate Algebraic Expressions
Take the expression to be equivalent to . What is the expression equivalent to?
When considering , begin at the right of the equation. Since
is equivalent to , must be equivalent to
Now we need only consider
Example Question #49 : How To Evaluate Algebraic Expressions
Quantity A:
Quantity B:
Quantity A is greater.
The two quantities are equal.
The relationship cannot be determined.
Quantity B is greater.
Quantity A is greater.
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.