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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
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 #121 : Arithmetic
If and
are integers such that
and
, what is the smallest possible value of
?
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.
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
The answer is
Make sure to distribute negatives throughout the second half of the equation.
Example Question #221 : Operations
Solve for :
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 #711 : Gre Quantitative Reasoning
Solve for :
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 .
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
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 :
Begin by isolating your variable.
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 #721 : Gre Quantitative Reasoning
Solve for :
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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