GRE Math : Negative Numbers
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Example Questions
Example Question #9 : Negative Numbers
Solve for 
To solve, you need to isolate the variable. We first subtract 
When dividing, if the signs of the numbers are the same (i.e. both positive, or both negative), you yield a positive result. If the signs of the numbers are opposites (i.e. one of each), then you yield a negative result.
Therefore:
Example Question #1 : How To Multiply Negative Numbers
x, y and z are negative numbers.
A
---
x + y + z
B
---
xyz
Quantity B is greater
The two quantities are equal
Quantity A is greater
The relationship cannot be determined
The relationship cannot be determined
Recognize the rules of negative numbers: if two negative numbers are multiplied, the result is positive. However if three negative numbers are multiplied, the result is negative. As such, we know B must be negative.
Since there are no restrictions on the values of x, y and z beyond being negative, lets check low values and high values: if every value was -1, multiplying the values would equal -1 while adding them would equal -3. However, if every value was -5, multiplying them would equal -125 while adding them would equal a mere -15. As such, we would need additional information to determine whether A or B would be greater.
Example Question #2 : How To Multiply Negative Numbers
Simplify:
Remember, the product of two negatives is positive. Also note that subtracting a negative is equivalent to adding its absolute value.
Example Question #2 : How To Multiply Negative Numbers
Quantity A:
Quantity B:
The two quantities are equal.
Quantity A is greater.
Quantity B is greater.
The relationship cannot be determined from the information given.
The relationship cannot be determined from the information given.
Imagine two different scenarios when x equals either extreme: –1 or 1. If x equals –1, then x squared equals 1 and x cubed equals –1 (a negative times a negative times a negative is a negative), and thus Quantity A is greater. The other scenario is when x equals 1: x squared equals 1 and x cubed also equals 1. In this scenario, the two quantities are equal. Because both scenarios are possible, the relationship cannot be determined without more information.
Example Question #4 : How To Multiply Negative Numbers
If 
This question tests your familiarity with the mathematical principles behind how negative numbers operate.
Which, of course, means that 
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