# GMAT Math : Solving equations

## Example Questions

### Example Question #51 : Equations

Solve for  in the equation

or

or

or

Explanation:

### Example Question #52 : Equations

Solve for  in the equation:

or .

or

or

or

or

or .

Explanation:

is a perfect square trinomial:

The equation can be rewritten as

By the square-root property, since no assumption was made about the sign of any variable,

Therefore,

or .

### Example Question #53 : Equations

Solve for  in the equation

or

or

or

or

or

or

Explanation:

The statement is a quadratic equation in , so it can be solved using the quadratic formula,

where

### Example Question #54 : Equations

How many distinct solutions are there to the following equation?

2

3

Infinitely Many

0

1

2

Explanation:

We are given a classic quadratic equation, but we aren't asked for the solutions, just how many distinct solutions there are. Remember, distinct solutions are different solutions. If we get two solutions that are the same numbers, they do not count.

The quickest way to solve this involves some factoring.

Start by pulling out a 3

Now, within our parentheses, we have a classic difference of squares. The interior factors further to look like this.

From here we can either solve the equation and count our solutions, or we can recognize that the two factors are different and therefore will give different solutions. Let's solve it by using the Zero Product Property

Solution 1

Solution 2

Thus, we have two distinct solutions!

### Example Question #55 : Equations

Solve for  in the equation

Explanation:

### Example Question #56 : Equations

is 44% of .

is what percent of ?

Explanation:

is 44% of , so  is  of .

Also,  is 300% of .

is  of

### Example Question #57 : Equations

Solve for :

Explanation:

To solve the equation, we first group the  terms on one side and the constants on the other side:

Now we can simply divide both sides by  to solve for :

### Example Question #58 : Equations

Solve the following equation:

Explanation:

To solve the equation, we must simplify it by adding together the like terms. We can group the  terms on the left side of the equation and the constants on the right side of the equation:

### Example Question #59 : Equations

Solve the following equation for :

Explanation:

To solve, we must isolate . First, subtract  from both sides and then divide both sides by .

Solve for :