# GRE Math : Negative Numbers

## Example Questions

### Example Question #1 : Negative Numbers

Quantity A:

Quantity B:

The relationship cannot be determined from the information given.

The two quantities are equal

Quantity B is greater

Quantity A is greater

Quantity A is greater

Explanation:

Since both quantities have an , you can ignore this variable, which will give you  and for quantities A and B, respectively. Since  and  are both negative numbers,  must be bigger than , which means that no matter what numbers they are, Quantity A must be bigger.

### Example Question #6 : Negative Numbers

If  and  are integers such that   and , what is the smallest possible value of ?

Explanation:

To make  as small as possible, let  be as small as possible , and subtract the largest value of  possible :

### Example Question #711 : Gre Quantitative Reasoning

Quantity A:

Quantity B:

Which of the following is true?

Quantity A is larger.

The two quantities are equal in size.

Quantity B is larger.

The relationship between the quantities cannot be determined.

Quantity B is larger.

Explanation:

A problem like this one is very easy.  All you need to do is manage your arithmetic well.  Remember that when you subtract a negative number, this is the same as adding the positive of that number.  Therefore, you can rewrite each of your quantities:

Quantity A:

Using a calculator, this comes out to be:

Quantity B:

Using a calculator, this comes out to be:

Therefore, quantity B is larger.

### Example Question #3 : Negative Numbers

Simplify

Explanation:

Make sure to distribute negatives throughout the second half of the equation.

### Example Question #7 : Negative Numbers

Solve for :

Explanation:

To solve this problem, you need to get your variable isolated on one side of the equation:

Taking this step will elminate the  on the side with :

Now divide by  to solve for :

The important step here is to be able to add the negative numbers.  When you add negative numbers, they create lower negative numbers (if you prefer to think about it another way, you can think of adding negative numbers as subtracting one of the negative numbers from the other).

### Example Question #4 : Negative Numbers

Solve for :

Explanation:

To solve this problem, first you must add  to both sides of the problem.  This will yield a result on the right side of the equation of , because a negative number added to a negative number will create a lower number (i.e. further away from zero, and still negative).  Then you divide both sides by two, and you are left with .

### Example Question #5 : Negative Numbers

Find the value of .

Explanation:

To solve for , divide each side of the equation by -2.

is the same as

which is POSITIVE

### Example Question #1 : How To Divide Negative Numbers

What is ?

45

Explanation:

A negative number divided by a negative number always results in a positive number.  divided by  equals . Since the answer is positive, the answer cannot be  or any other negative number.

### Example Question #1 : How To Divide Negative Numbers

Solve for :

Explanation:

Subtract  from both sides:

, or

Next, subtract  from both sides:

, or

Then, divide both sides by :

Recall that division of a negative by a negative gives you a positive, therefore:

or

### Example Question #1 : Negative Numbers

Solve for :

Explanation:

To solve this equation, you need to isolate the variable on one side. We can accomplish this by dividing by  on both sides:

Anytime you divide, if the signs are the same (i.e. two positive, or two negative), you'll get a positive result.  If the signs are opposites (i.e. one positive, one negative) then you get a negative.

Both of the numbers here are negative, so we will have a positive result:

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