GRE Math : How to multiply negative numbers
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Example Questions
Example Question #1 : How To Multiply Negative Numbers
x, y and z are negative numbers.
A
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x + y + z
B
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xyz
The two quantities are equal
Quantity B is greater
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 #1 : 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:
Quantity B is greater.
The relationship cannot be determined from the information given.
The two quantities are equal.
Quantity A is greater.
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 #3 : 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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