### All GRE Math Resources

## Example Questions

### Example Question #51 : How To Evaluate Algebraic Expressions

Quantity A:

Quantity B:

**Possible Answers:**

The two quantities are equal.

Quantity B is larger.

Quantity A is larger.

The relationship cannot be determined.

**Correct answer:**

Quantity A is larger.

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 : Evaluating Expressions

The expression is equivalent to . Evaluate

**Possible Answers:**

**Correct answer:**

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:**

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 #94 : 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 two quantities are equal.

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 #54 : 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.

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 #55 : How To Evaluate Algebraic Expressions

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

**Possible Answers:**

**Correct answer:**

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 : Evaluating 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 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:

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 #52 : Evaluating Expressions

Quantity A:

Quantity B:

**Possible Answers:**

The relationship cannot be determined.

Quantity B is greater.

Quantity A is greater.

The two quantities are equal.

**Correct answer:**

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:

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 #53 : Evaluating 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:**

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:

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 #52 : Evaluating Expressions

Quantity A:

Quantity B:

**Possible Answers:**

The two quantities are equal.

Quantity A is greater.

Quantity B is greater.

The relationship cannot be determined.

**Correct answer:**

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 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.