# GRE Math : How to evaluate algebraic expressions

## Example Questions

### Example Question #361 : Algebra

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.

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 #362 : Algebra

Quantity A:

Quantity B:

The relationship cannot be determined.

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

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 #363 : Algebra

Quantity A:

Quantity B:

The two quantities are equal.

Quantity B is greater.

Quantity A is greater.

The relationship cannot be determined.

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 #364 : Algebra

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?

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 #361 : Algebra

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

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 #366 : Algebra

Quantity A:

Quantity B:

The two quantities are equal.

The relationship cannot be determined.

Quantity A is greater.

Quantity B is greater.

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 #367 : Algebra

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

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 #368 : Algebra

Quantity A:

Quantity B:

The two quantities are equal.

The relationship cannot be determined.

Quantity A is greater.

Quantity B is greater.

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 #369 : Algebra

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

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 #370 : Algebra

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.

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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